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Birthdays |
The Birthday applet above simulates birthdays of various sized groups of randomly selected people.
Type into the box the number of people in your group, up to 100 maximum, and press the Enter key.
The applet assigns a birthday to each person in the group.
Birthdays displayed in red are duplicates.
ASSIGNMENT
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? |
||
2. What is the probability that two randomly selected people will NOT have the same birthday? | ||
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | ||
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | ||
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | ||
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | ||
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? |
PRIVATE |
For 7 points, copy the table to a comment and answer the first 6 questions.
Send #7 to me privately.
YOU WILL NOT RECEIVE YOUR OTHER POINTS TILL YOU ANSWER THE 7th QUESTION!
There is nothing wrong with researching the internet for answers to this assignment.
Show us your arithmetic and reasons in the HOW box.
Use only the 4 operators + - x /
Do NOT use the ! sign.
You can use ... to mean and so on...
Give answer in both fractions and decimals.
Comments:
From TBird - 12/15/06 2:21 PM
From Houdini - 12/15/06 8:44 AM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .00274=.274% | 1 day possible/365 total days |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .99726=99.726% | 1-.00274 or 364/365 |
3a. What is the probability that three randomly selected people three randomly selected people | A. .0082=.82% B. .9918=99.18% | A. First answer part B, Then subtract from one. B. 364/365x363/365=.9918 |
4a. What is the probability that no two people in our class have the same birthday? at least one member of our class | A. .833=83.3% B. .167=16.7% | A. (364x363...x354)/365^11= .833 B. Solve part A, then subtract from 1 |
5. How many people must be in a classroom so have the same birthday is roughly 50%? | 22 Students | (364x363...x343)/365^22= .4927=49.27% |
6. How many people must be in a classroom so have the same birthday is 100%? | 366 Students | (366x365)/365^2=1.003=100.3% |
7. What is the probability that at least 2 out of 3 randomly selected people | PRIVATE |
Fixed!!!
From wHolt - 12/14/06 11:56 AM
From Spartan - 12/14/06 11:28 AM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0027 or .27% | 1 day 1/365= .0027 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9972 or 99.7% | 1 day 364/365= .997 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | 3a. .0082 or .82% 3b. .9918 or 99% | 3a. 365/365 x 364/365 x 363/365 = .0082 3b. 365/365 x 364/365 x 363/365 = .9918 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | 4a. .8056 or 81% 4b. .1944 or 19% | 4a. continue 3a. down to 352/365= .8056 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 | square root of 365= 19.1x 1.2=22.92= 23 people |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 1 person greater than the number of days to be 100% |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Houdini - 12/14/06 8:38 AM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .00274=.274% | 1 day possible/365 total days |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .99726=99.726% | 1-.00274 or 364/365 |
3a. What is the probability that three randomly selected people three randomly selected people | A. .0082=.82% B. .9918=99.18% | A. First answer part B, Then subtract from one. B. 364/365x363/365=.9918 |
4a. What is the probability that no two people in our class have the same birthday? at least one member of our class | A. .8056=80.56% B. .1944=19.44% | A. (364x363...x353)/365^12= .8056 B. Solve part A, then subtract from 1 |
5. How many people must be in a classroom so have the same birthday is roughly 50%? | 22 Students | (364x363...x343)/365^22= .4927=49.27% |
6. How many people must be in a classroom so have the same birthday is 100%? | 366 Students | (366x365)/365^2=1.003=100.3% |
7. What is the probability that at least 2 out of 3 randomly selected people | PRIVATE |
From wHolt - 12/13/06 11:16 AM
From Bubba - 12/12/06 6:51 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .00000005 | 1/365*1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9945279 | 364/365*364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | .000000000000000000000125 .983673367779332952639 | .00000005*.00000005*.00000005 .9945279*.9945279*.9945279 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | ..94660699888352112337344653388636 .0000825 | .9973to the 11th power 1/365*11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | .5=x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 366/365 |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From wHolt - 12/3/06 1:26 PM
Don't round off till the last step in your calculation.
Also, I don't suppose any of you will read this, but
1/365 is the correct way to write a probability, not 1:365.
1:365 is the way to write 1 to 365 odds.
they are not the same.
From SuperDuke - 12/2/06 9:35 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | 1:365 or .27% | 1 day in which it would be true, out of 365 choices. or 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 364:365 or 99.73% | 1 day this would be false which is 364 days which it would be true, out of 365 choices. or 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | 3a. 1:133,225 or .00075% 3b. 132,132:133,225 or 99.18% | 3a. 1st guy is 1 (anyday of year) * by 2nd guy 1:365 * 3rd guy 1:365 = 1:133,225 or 1/133,225 for decimal. 3b. 1st guy is 1 (anyday of year) * by 2nd guy is 364:365 * 3rd guy is 363:365 = 132,132:133,225 or 132,132/133,225 = 99.18% |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | 4a. see "how" 4b. 17.82% | 4a. 1 * 364:365 * 363:365 * . . . 354:365 = 12760085554611260002468531200:15318685818767563885595703125 or as a decimal 0.83297521116193560885420951999913 which is ruffly 83% 4b. Question 1 shows us how we have a .27% chance of 1 persons birthday being the same as another. Basically it is a question of how do we combine these 11 other people that 1 would have a chance of hitting on. first we realize it is a .27% chance for each person to hit on each of the other persons birthday. with this assumption in mind can find it as 11+10+9+8+7+6+5+4+3+2+1 =66, this represents the # of different possible connections between students. Each of those connections has a .27% chance. (.27*66=17.82%) |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 people | I agree with the reasoning of finding the opposite first. that and this added must equal one. As stated by others it is (365/365*364/365*363/365*362/365*361/365*360/365*359/365*358/365*357/365*356/365*355/365*354/365*353/365*352/365*351/365*350/365*349/365*348/365*347/365* and if you subtracted it from 1 u get .502... |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 365/366 = greater than one |
From Cheana - 12/2/06 1:52 AM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | 0.002739726027397260273972602739726 | 365/365*1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 0.99726027397260273972602739726027 | 365/365*364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a. 7.5060987051979733533495965471946e-6 b. 0.99179583411521861512478889097392 | a. 365/365*1/365*1/365 b.365/365*364/365*363/365 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a. 0.8329752112 b. 0.1670247888 | a. 365/365*364/365*363/365*362/365*361/365*360/365*359/365*358/365*357/365*356/365*355/365*354/365 b.1-.8329752112 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 people | 365/365*364/365*363/365*362/365*361/365*360/365*359/365*358/365*357/365*356/365*355/365*354/365*353/365*352/365*351/365*350/365*349/365*348/365*347/365* |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | There has to be at least one more than the number or days in a year in the room |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Fro - 11/30/06 9:59 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0027 | 1 - 365/365 * 364/365= .0027 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9972 | 365/365 * 364/365= .9972 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | 3a. .0082 3b. .9918 | 3a. 1 - 365/365 x 364/365 x 363/365, = .0082 3b. 365/365 x 364/365 x 363/365, = .9918. |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | 4a. .8056 4b. .1944 | 4a. 365/365 x 364/365 x 363/365.....353/365 = .8056 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 | 1.2 multiplied by the square root of 365 = 23 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | There must be one more person than there are days in a year |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From wHolt - 11/29/06 1:04 PM
A NOTE ON at least PROBLEMS
When you see a problem that says at least one,
it means 1 or 2 or 3 or ... all
adding up all those probabilities is clumsy.
so approach it another way:
at least 1 = not none
Observe how some of your fellow travelers have used this idea .
From Trixie - 11/28/06 10:20 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .27% | 1/365 * 1 = .0027 = .27% |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 99.73% | 365/365 * (364*365) = .9973 = 99.73% |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | A. B. 99.20% | A. 1 - 365/365 * 364/365 * 363/365 = .008 = .80% B. 365/365 * 364/365 * 363/365 = 1 * .997 * .995 = .9920 = 99.20% |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | A. 83.30% B. 16.70% | A. 365/365 * 364/365 * 363/365 * 362/365 * 361/365 * 360/365 * 359/365 * 358/365 * 357/365 * 356/365 * 355/365 * 354/365 = 1 * .9972 * .9945 * .9917 * .9890 * .9863 * .9835 * .9808 * .9780 * .9753 * .9726 * .9698 = .8330 = 83.30% B. 1 - (365/365) * (364/365) * (363/365) * (362/365) * (361/365) * (360/365) * (359/365) * (358/365) * (357/365) * (356/365) * (355/365) * (354/365) = .1670 = 16.70% |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 | A. 365/365 * 364/365 * 363/365 * 362/365 * 361/365 * 360/365 * 359/365 * 358/365 * 357/365 * 356/365 * 355/365 * 354/365 * 353/365 * 352/365 * 351/365 * 350/365 * 349/365 * 348/365 * 347/365 * 346/365 * 345/365 * 344/365 * 343/365 * 342/365 * 341/365 = 49.22 is as close to 50% as you can get so therefore, there can be 23 people in the classroom. |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 366 since there are 365 days a year, there would nee to be 366 people to ensure that 2 people had the exact same birthday. |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From David - 11/28/06 7:52 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .27% | (365/365)*(1/365)=1/365=.27%-probablility of one person having a birthday is 365/365. The probability of the second having the same birthday is 1/365. Multiply these together to get the number. |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 99.73% | um, since the probability of anything happening is 100% then subtract .27% from one and get 99.73% |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | b. 98.36% a.1.64% | Ill answer it the other way around. the probability that three random people have different birthdays is 1*(365/365)*(364/365)= 47831784/48627125=98.36% subtract that from 1 and get the probability that three people have the same birthday. 1-.9836=1.64% |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a. 83% b.17% | 365/365*364/365*363/365....354/365=.83 1-.83=.17 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 | 365/365*364/365*363/365...343/365=.493 to get a 50% chance that two people have the same birthday in a group, you need a group of 23 people. |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | A more interesting question would be what is the chance of 365 people having all different birthdays. if I had a calculator I would compute ((365-1)/365)*((365-2)/365)*...((365-364)/365) |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Melewen - 11/28/06 6:41 PM
| Questions | Answers | How? |
| 1. What is the probability that two randomly selected people will have the same birthday? | .27% | Since the first guy can have any birthday, his probability is figured as 365/365. Then, the second guy has to have that one specific birthday, so his would be 1/365. Then you multiply them to get .002739726 |
| 2. What is the probability that two randomly selected people will NOT have the same birthday? | 99.7% | Again, the first guy can have any birthday, so 365/365. The second guy can have any birthday besides the first guy's, so his is 364/365. Then, you multiply them to get .997260274 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a) .8204% b) 99.1796% | a) You find the probability that they will have different birthdays (see the B part to this question) b) Again, same logic as #2: 365/365 x 364/365 x 363/365 (363 because he can't have the two |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a) 80.55897248% b) 19.44102752% | a) 365/365 x 364/365 x 363/365 x 362/365 x 361/365 x 360/365 x 359/365 x 358/365 x 357/365 x b) Again, you subtract the probability that no one will have the same birthday (.8055897248) |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 22 | I used the same method as #4 to figure this out. If you can find the opposite probability of something, you can subtract it from one to find the original probability you were after. So, I did 365/365 x 364/364 ... 343/365 to find that you have to have 22 people in a class for the probability to be 50% |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 44 | You would double the number it took to get 50%. So, 46 |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Kathi - 11/28/06 6:21 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0027 or .27% | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9973 or 99.73% | 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | .008 or .8% .9918 or 99.2% | 1-(364/365)(363/365) = .008 (365/365)(364/365)(363/365) = .9918 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | .80 or 80%
.2 or 20% | 365/365 * (365-1)/365*(365-2)/365* (365-3)/365 *(365-4)/365*(365-5)/365* (365-6)/365 *(365-7)/365* (365-8)/365* (365-9)/365 *(365-10/365*(365-11)/365*(365-12) = .800 1-.80 = .2 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 366 people to have 100% chance of having the same birthday, we would have to divided that by 2 = 183 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 365 days in the year, we need 366 to be sure that we would get 2 people with the same birthday. |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? |
From wHolt - 11/28/06 10:35 AM
You are looking for the probability that the second guy has the same birthday as the first.
From DirtyBird - 11/27/06 7:41 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0027 or .27% | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9973 or 99.73% | 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a).82% b)99.18% | a) 3/365=.0082 b)100%-.82%=99.18% |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a).98% b).66% | a).0082*12=.0984 b).0055*12=.066 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 365/2=183 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | You need 1 more person than days in the year unless... there is a pair of twins in the classroom that you are not telling us about. Is that the trick? |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Draco - 11/27/06 1:34 PM
From Draco - 11/27/06 1:03 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | approx. .27% | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | approx. 99.73% | 100-.27 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a.approx. .8% b.approx. 99.2% | (365/365)-(364/365*363/365) 1-.997*.995 1-.992=.8 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a.approx. 16.8% b.approx. 83.2% | (365-365)-(364/365*363/365...*354/365) 1-(.997*.995*.992*.99*.986*.983*.98*.978*.975*.972*.97) 1-.832=.168 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 366/2 *see explanation below for how I got 366 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | With 366 people, at least two must have the same birthday assuming that there are 365 possible birthday choices. |
From wHolt - 11/27/06 9:58 AM
Careful - watch those percents %
.777 is not .777%
also if 365 people are in a room, they possibly could all have different birthdays.
Most of you are copying the guy directly above you without thinking,
and thus without earning any points either.
From Zonino - 11/26/06 11:25 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | 0.27% | The probability that one person has a birthday is 365/365 or 1 (100%). The probabilty that someone shares the same date is 1/365. Multiplying the two people together 1*1/365 gives us the total odds which is 1/365. Dividing 1 by 365 gives us 0.0027 or .27%. |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 99.73% | The odds of a person having a birthday is 365/365 or 1. The odds of a person having a different birthday is 364/365. Multiplying the two together gives us 364/365 or 0.9973 or 99.73% |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | 3A - 0.80%
3b 99.20% | The easiest way to do this is 3b first. The odds of a person having a birthday is 365/365. The second person does not have the same birthday as the first, leaving 364/365. The Third person is different than the other two, which would be 363/365. Multiplying this all together gives us 365/365*364/365*363/365 which is 1*0.9973*0.9945 or 0.9920 or 99.20% To find 3A, all we have to do is subtract 99.20% from 100% which leaves us with 0.80%. |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | 4A - 83.30% 4B - 16.70% | 4A - This would be 365/365 *364/365 *363/365 *362/365 *361/365 *360/365 *359/365 *358/365 *357/365 *356/365 *355/365 *354/365 or 1 *0.9973 *0.9945 *0.9918 *0.9890 *0.9863 *0.9836 *0.9808 *0.9781 *0.9753 *0.9726 *0.9699 or 0.8330. This is 83.30% 4B - To find the probability that at least 1 person has the same birthday, we can simply subtract the probability of not having the same birthday from 100%. So 100%-83.30% = 16.70% |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 | The easiest way to determine this is to figure out how many people would take to have the probability of nobody having the same birthday to be 50% and then we would also have the probabilty of having two people having the same birthday. Thus 365/365*364/365*363/365...343/365 = 0.4927. 1-0.4927 is .5073 or 50.73% which is as close to 50% as we can get. |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | To have exactly 100% you must have 366 people (if we don't take into consideration leap year, which would otherwise be 367). If we have less than that, then we will have some percentage of 99.999...% since 100% is the most you can have as a probability. (basically if you have 365 people they could each all have a different birthday, but with 366 someone must share a birthday) |
From BassLady - 11/26/06 9:33 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .003% | 1 - .997 (see answer below for how I came up with .997% |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .997% | (365 * 364) / (365 * 365) |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | A. .008% B. .992% | A. (365 * 364 * 363) / (365^3) B. 1 - .008 = .008% |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | A. .83% B. .14% | (365 * 364 * 363 * 362 * 361 * 360 * 359 * 358 * 357 * 356 * 355 * 354) / (365 ^12) |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 365 / 2 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 365 | 365 / 365 |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Bubba - 11/26/06 7:19 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0027 | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .997 | 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | .0000072 .995 | .0027*.0027 .9973*.9973 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | .9681 .0301 | .9973*11 11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | .5=x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 366/365 |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From JooJoo - 11/26/06 7:05 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | 27% | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 99.73% | 364/365=99.73 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | 3a. 80% 3b. 99% | 3a. 1-(364/365)(363/365) 3b. (365/365)(364/365)(363/365) |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | 4a. 96.8% 4b. about 3% | 4a. .9973x 11 4b. 11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | .5=x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 367 | Because you would have to have more people than there are days in the year. So you would need 366 people then when you take into account leap year you need one more person so that would make 367 people |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Harkar - 11/26/06 6:43 PM
| Questions | Answers | How? |
| 1. What is the probability that two randomly selected people will have the same birthday? | .0027 | 1/365 … because there would only be one day out of 365 days for the second person to match the first person's birthday. |
| 2. What is the probability that two randomly selected people will NOT have the same birthday? | 0.9973 | 364/365 …. because there are 364 days in the year for the 2nd person to not match the 1st person's birthday. |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a.0.00000729
| a.(1/365)(1/365)
|
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a. .9681
| a. b. |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | .5 = x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | Since it takes 183 people to have a 50% chance that two people will have the same birthday, then it would take 366 (183 x 2) people to have a 100% chance of two people having the same birthday. |
From 7Iron - 11/26/06 6:24 PM
Questions | Answers | How? |
| 1. What is the probability that two randomly selected people will have the same birthday? | .002739 = .27% | 1/365 |
| 2. What is the probability that two randomly selected people will NOT have the same birthday? | .9972 = 99% | 1 – 1/365) |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | .000007506 .9945 | 1/365 * 1/365 1-(1/365)*1-(1/365) |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | .969871 .030129 | 1-(.002739)*11) .002739 *11 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 182.5~183 | 365/x=.5 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 366/365 = 1.0027 which is greater than 1 |
From GolfGirl - 11/26/06 3:08 PM
| Questions | Answers | How? |
| 1. What is the probability that two randomly selected people will have the same birthday? | 0.0027 | 1/365 There is only one chance they will have the same birthday at the same time. |
| 2. What is the probability that two randomly selected people will NOT have the same birthday? | 0.9973 | 364/365, all the other days have a chance of not being the same. |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a.0.00000729 b.0.99460729 | a)(1/365)(1/365) b)(364/365(364/365) |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a. 0.9681 b. 0.0301 | a)0.9973*11 b)11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 0.5=x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | There has to be one more person than there are days in a year to be 100%. |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From RockClimber - 11/26/06 12:21 PM
1. What is the probability that two randomly selected people will have the same birthday? | .0027 | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9973 | 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | A. .00000729 B. .9946 | A. .0027 X .0027 B. .9973 X .9973 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | A. .9681 B. .0301 | A. .9973 x 11 B. 11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | half of 365. |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 or 367 for a leap year. | you have to add one more so that every day of the year is covered in order to have two people to have the same day/ 367 is for a leap year |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Tiger - 11/25/06 1:01 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0027 | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9972 | 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a. .0000072 b. .9944 | a. .0027*.0027 b. .9972*.9972 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a. .9681 b. .0301 | a. .9973*.9973*.9973*.9973*.9973*.9973*.9973*.9973*.9973*.9973*.9973 =.96807 b. .11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 365*.5=182.5 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | so there is one more person than there are days in a year |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From wHolt - 11/24/06 4:33 PM
I hope you are all in a holiday mood
and are willing to help a neighbor in distress...
From CenterField - 11/24/06 10:19 AM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .003% | 365/365 * 364/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .997% | 100% - .003% |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? |
a. .008% b. .992% | a. 365/365 * 364/365 * 363/365 b. 100% - .008% |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a. 83% b. 17% | a. 365/365 * 364/365 * 363/365 ... 354/365 = .83 b. 100% - 83% = 17% |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 23 | 365/365 * 364/365 * 363/365 ... 343/365 = .493 (odds of not having same birthday) 1 - .493 = .507 (odds of having same birthday) = just over 50% |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 367 | Taking into account leap years, which have 366 days, at least one person would have to have the same birthday as at least one other. Having 50 people in a room would give you a 97% chance, having 100 people would give you a 99.9994% chance. The increments are so small that to truly have a full 100%, you must have this many people. |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Kathi - 11/24/06 9:43 AM
| Questions | Answers | How? |
1. What is the probability | 0.0027 | 1/365 there is only one day out of the year for |
2. What is the probability that two | 0.9973 | 364/365 there are 364 days of the year that |
3a. What is the probability that
| 3a. 0.00000729
3b. 0.99460729 | 3a. There is 0.0027 probability that the 2nd 3b. There is 0.9973 probability that the 2nd |
4a. What is the probability that | 4a. 0.9681 4b. 0.0301 | 4a. There is 0.9973 probability that 2 people 4b. 11 different birthdays; 365 days |
5. How many people must be | 183 people | 0.5=x/365 |
6. How many people must be | 366 | With 365 days in a year, the only way to make sure |
7. What is the probability that | PRIVATE |
From Sunshine - 11/22/06 12:43 AM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0027 | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9973 | 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a. .00000729 b. .9944 | a. .0027 x .0027 b. .9972 x .9972 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a .9681 b. .0301 | a. .9973 x 11 b. 11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | .5 = x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | you have to add one more to how many days are in a year so that two people have to have the same bday. |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From TBird - 11/20/06 9:43 PM
| Questions | Answers | How? |
| 1. What is the probability that two randomly selected people will have the same birthday? | 0.0027 | 1/365, because therer is only one chance they will have the same birthday together. |
| 2. What is the probability that two randomly selected people will NOT have the same birthday? | 0.9973 | 364/365, because all of the other days has a chance of not being the same |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | a.0.00000729 b.0.99460729 | a)(1/365)(1/365) b)(364/365)(364/365) |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | a. 0.9681 b. 0.0301 | a)0.9973*11 b)11/365 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 0.5=x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | because there has to be one more person than there are days in a year to account for the 100% |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | private | private |
From wHolt - 11/20/06 11:24 AM
In these last assignments you will apply all those previous techniques.
From Pac - 11/19/06 4:52 PM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | 0.0027 | 1/365 because it would be only one day out fo the year for the second person to match the first person's birthday |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 0.9973 | 364/365 because there are 364 OTHER days in the year for the 2nd person to not match the 1st person's birthday |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | 3a. 0.00000729 3b. 0.99460729 | 3a. There is 0.0027 probability that person B will match person A and then 0.0027 probability that person C will match person A (or B) so 0.0027 * 0.0027 = 0.00000729 3b. Same logic as above but using 0.9973 so 0.9973*0.9973 = 0.99460729 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | 4a. 0.9681 4b. 0.0301 | 4a. There is 0.9973 probability that people don't have the same birthday so I'm going with 0.9973*0.9973*0.9973*0.9973*0.9973*0.9973*0.9973*0.9973*0.9973*0.9973*0.9973*0.9973 = 0.96807683593304330602821225474879 4b. You've got 11 people with 11 different birthdays so that's 11 of 365 days and then 1 person matches one of those 11 people. So that's 11/365=0.0301369863 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 people | 0.5=x/365 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | With 365 days in a year, the only way to make sure that there is 100% chance is to have more people than there are days in the year. With 366 people, at least two of them have to have the same birthday. |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
From Boki - 11/18/06 6:04 PM
From wHolt - 11/18/06 1:47 PM
How many people are required for a 100% chance?
From Boki - 11/17/06 11:16 PM
| Questions | Answers | How? |
| 1. What is the probability that two randomly selected people will have the same birthday? | 0.27 or 27% | There would have to be 366 people in order to be absolutely certain that two of them have the same birthday. 365/365*364/636*….365-n+1)/365 or 365/365*364/636*………(366-n)/365 The first person can have any birthday which is 365 possible birthdays out of 365 days (if do not count leap year.) So the probability for the first person is 365/365 or 100%. The second person will have chance of 1/365=0.002739726027397260273972602739726 to have the same birthday as first person which is approximately .27%. |
| 2. What is the probability that two randomly selected people will NOT have the same birthday? | 99.73% | The probability that two randomly selected people will NOT have the same birthday is 99.73%. All we have to do is to deduct the probability that two randomly selected people will have the same birthday from 100%. So, here we have 100%-.27%=99.73% Or We can do it this way: the probability for the first person is 365/365=1 or 100%, and the probability for the second person 364/365=0.9973 or 99.73%. |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | 3a. .80%
3b. 99.20%
| 3a. the probability that three randomly selected people will have the same birthday is 1 - (364/365) (363/365) =1-.997*.995=1-.992= .008, which is approximately .80%. 3b.The probability that three randomly selected people will not have the same birthday is 365/365 x 364/365 x 363/365= 0.9918 or approximately 99.20% . |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | 4a. 80.05% 4b. 19.95 % | 4a. 365 / 365 x (365 - 1) / 365 x (365 - 2) / 365 x(365 -3) / 365 x (365 - 4) / 365 x(365 -5) / 365 x (365 - 6) / 365 x(365 -7) / 365 x (365 - 8) / 365 x(365 -9) / 365 x (365 - 10) / 365 x(365 -11) / 365 x (365 - 12) / 365 =1*.99*.99*.99*.99*.99*.98*.98*.98*.98*.97*.97*.97 =0.800562934224474496214832 or 80.05% which is the probability the probability that no two people have the same birthday. 4b. the probability that at least one member of our class has the same birthday as another is: 1-0.8005=0.1995 or 100-80.05=19.95 which is the probability 19.95 % that at least one member of our class has the same birthday as another. |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | must be 23 people | we can do it by adding the terms to the numerator and denominator until we find how many term we will need to get 50% 365 / 365 * (365 - 1) / 365 * (365 - 2) / 365 *(365 -3) / 365 * (365 - 4) / 365 *(365 -5) / 365 * (365 - 6) / 365*(365 -7) / 365 * (365 - 8) / 365 *(365 -9) / 365 * (365 - 10) / 365 *(365 -11) / 365 * (365 - 12) / 365*(365 - 13) / 365 * (365 - 14) / 365 *(365 -15) / 365 * (365 - 16) / 365 *(365 -17) / 365 * (365 - 18) / 365 *(365 -19) / 365 * (365 - 20) / 365 *(365 -21)/365*(365-22+1)/365= 1*.99*.99*.99*.99*.99*.98*.98*.98*.98*.97*.97*.97*.96*.96*.96*.96*.95*.95*.95*.95*.94*.94= =0.4893623342472468857313253839085 which is approximately .50 or 50% Since last term used is (365-22+1)/365, it means that in our classroom must be 23 people so the chance that two of them have the same birthday is roughly 50%. |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | must be 48 people | 365 / 365 * (365 - 1) / 365 * (365 - 2) / 365 *(365 -3) / 365 * (365 - 4) / 365 *(365 -5) / 365 * (365 - 6) / 365*(365 -7) / 365 * (365 - 8) / 365 *(365 -9) / 365 * (365 - 10) / 365 *(365 -11) / 365 * (365 - 12) / 365*(365 - 13) / 365 * (365 - 14) / 365 *(365 -15) / 365 * (365 - 16) / 365 *(365 -17) / 365 * (365 - 18) / 365 *(365 -19) / 365 * (365 - 20) / 365 *(365 -21)/365*(365-22)/365*(365 - 23) / 365 * (365 - 24) / 365 *(365 -25) / 365 * (365 - 26) / 365 *(365 -27) / 365 * (365 - 28) / 365*(365 -29) / 365 * (365 - 30) / 365 *(365 -31) / 365 * (365 - 32) / 365 *(365 -33) / 365 * (365 - 34) /365*(365 - 35) / 365 * (365 - 36) / 365 *(365 -37) / 365 * (365 - 38) / 365 *(365 -39) / 365 * (365 - 40) / 365*(365 -41) / 365 * (365 - 42) / 365 *(365 -43) / 365 * (365 - 44) / 365 *(365 -45) / 365 * (365 - 46) /365*(365-47)/365*(365-48)/365=1*.99*.99*.99*.99*.99*.98*.98*.98*.98*.97*.97 in a classroom must be 48 people |
From wHolt - 11/17/06 2:54 PM
From Pod - 11/16/06 12:46 AM
1. What is the probability that two randomly selected people will have the same birthday? | .0027 | 1/365 |
2. What is the probability that two randomly selected people will NOT have the same birthday? | .9972 | 364/365 |
| 3a. What is the probability that three randomly selected people will have the same birthday? 3b. What is the probability that three randomly selected people will NOT have the same birthday? | .00000729
.9944 | .0027 * .0027
.9972 * .9972 |
| 4a. What is the probability that no two people in our class have the same birthday? Assume there are now 12 members left in our class. 4b. What is the probability that at least one member of our class has the same birthday as another? | .0907
.0297 | .9972 *11
.0027 * 11 |
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 183 | 365/183= 50.14%chance |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 366 | 365 days in a year, one extra to have the same b'day |
From wHolt - 11/13/06 10:19 AM
Kathi - thanks for going first, as usual...
Here are some ideas to consider:
If the chance that any 2 people have the same birthday is 2/365,
then is the chance that any 365 people all have the same birthday 365/365 =1 ?
And what if you have 1 million people.
Is the chance that they all have the same birthday 1million/365 > 1 ?
Is it possible to have a probability greater than 1? What would it mean?
Recheck your thinking about this.
Also is it necessary for the first person you choose to have a specific birthday?
Question 1 is actually asking,
what is the probability that the second person has the same birthday as the first?
From Kathi - 11/13/06 5:05 AM
| Questions | Answers | How? |
1. What is the probability that two randomly selected people will have the same birthday? | .0056 | 2/356=.0056 2 people 356 days in the year |
2. What is the probability that two randomly selected people will NOT have the same birthday? | 354:2 | There are 354 ways not to have the same birthday against 2 ways to have the same birthday. |
3a. What is the probability that three randomly selected people
| .0084
353:3 | There are 3 ways to get the same birthday from a 356 day year 3/356 = .0084
There are 353 ways not to have the same birthday against 3 ways to have the same birthday. |
4a. What is the probability that no two people in our class have the same birthday?
| 344:12
| There are 344 ways not to have the same birthday against 12 ways to have the same birthday. There are 12 ways to get the same birthday from a 356 day year.
|
| 5. How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%? | 178 | 178/356 = .5 |
| 6. How many people must be in a classroom so the chance that two of them have the same birthday is 100%? | 357 | 357/356 = 1.0 |
| 7. What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week? | PRIVATE |
Last Modified 12/14/06 11:57 AM
1. What is the probability that two randomly selected people will have the same birthday?
2. What is the probability that two randomly selected people will NOT have the same birthday?
3a. What is the probability that three randomly selected people
will have the same birthday?
3b. What is the probability thatthree randomly selected people will NOT have the same birthday?
A. .0082=.82%
B. .9918=99.18%
A. First answer part B,
Then subtract from one.
B. 364/365x363/365=.9918
4a. What is the probability that no two people in our class have the same birthday?
Assume there are now 12 members left in our class.
4b. What is the probability that t least one member of our class
has the same birthday as another?
A. .833=83.3%
B. .167=16.7%
A. (364x363...x354)/365^11=
.833
B. Solve part A,
then subtract from 1
5. How many people must be in a classroom so
the chance that two of them have the same birthday is roughly 50%?
(364x363...x343)/365^22=
.4927=49.27%
6. How many people must be in a classroom so
the chance that two of themhave the same birthday is 100%?
7. What is the probability that atleast 2 out of 3 randomly selected people
were born on the same day of the week?