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Powerball

Tennessee Powerball

TENNESSEE POWERBALL LOTTERY

lottery ticket


  A                      PICK 5
 



PROBABILITY

Now that you know all about how to count, you can compute probabilities.
A probability is a measure of chance.
A probability is a number between 0 and 1 inclusive.
If it's more or less, you counted wrong!
The bigger the number, the better the chance.
The smaller the number, the less of a chance.
A probability is the quotient of two counts:
The first count is the number of ways something can happen that you want
divided by the total number of ways something can happen whether you like it or not.
We can concoct a probability formula like this;

P(x) = WAYS WANTED / WAYS TOTAL
P(x) = YOUR COUNT / TOTAL COUNT
P(x) = SOME WAYS / ALL WAYS,

where P(x) means the probability of an event x.
For example: what is the probability of drawing an Ace from a deck of cards.
There are 4 ways to draw an Ace from a deck of cards with 52 cards
4 ways you want and 52 ways total.
Therefore, P(Ace) = 4/52 = .077

There are thus 48 ways not to draw an Ace against 4 ways to draw one.
We call these the Odds of drawing an Ace.
We write Odds like this 48 to 4 or 48:4.

Since the number of some is always less than or equal to the number of all,
probability is always less than or equal to 1,
but probability cannot be negative either.
So probability can never be less than 0.
For more about probability,
read the Wikipedia on Probability.



ASSIGNMENT

Find the probabilities for winning the Jackpot in the Tennessee Powerball Lottery.
To win the Jackpot, you must guess the correct 5 numbers from 55, plus pick the correct Powerball number.
The order of the numbers does not matter.

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?    
2. How many ways can you pick a Powerball number?   
3. How many ways can you choose all 5 numbers and a Powerball number?    
4. How many ways can you win the Jackpot?    
5. What are your chances of winning the Jackpot?   
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game for the Jackpot. 		  


Copy this table to a comment below and answer as many of the 6 questions as you can.
Show us your arithmetic and reasons in the HOW box.
Then send me the answer to question #7 privately in an email:

7. In 2005, Powerball changed from 53 to 55 balls.
What was the probability of winning the Jackpot before the change?
Are your chances of winning better now with more balls?
Show arithmetic in answer.
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.
Tell me if you are counting order, or not counting order,
so I will know if you understand what you are doing.

YOU WILL NOT RECEIVE YOUR OTHER POINTS TILL YOU ANSWER THIS 7th QUESTION!


 

   POWERBALL PRIZES

IF YOU MATCHYOU WIN
5 of 5 + POWERBALL JACKPOT
5 of 5 $200,000
4 of 5 + POWERBALL$10,000 
4 of 5$100 
3 of 5 + POWERBALL $100 
3 of 5 $7 
2 of 5 + POWERBALL $7 
1 of 5 + POWERBALL $4 
POWERBALL ONLY$3

Comments:

From Spartan - 12/14/06 11:54 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   3,478,761

55 possibilities for the first, 54 possibilities for the second, ..., and 51 for the fifth number drawn.
55 x 54 x 53 x 52 x 51 / (5x4x3x2x1=120)

2. How many ways can you pick a Powerball number?   42 You are only allowed one choice from 42 numbers, therefore you have 42 options.
3. How many ways can you choose all 5 numbers and a Powerball number?   146,107,962

 Each combination of numbers can have a different powerball, so you need to multiply 3,478,761 by 42 powerball choices.

3,478,761 x 42 =146,107,962

4. How many ways can you win the Jackpot?  1

To win the Jackpot, you have to match all the numbers and the powerball, so you have no room for error... only 1 way to win.

5. What are your chances of winning the Jackpot?  146,107,962 to 1 All combinations to the chance to the # of ways to win.
 146,107,962 to 1

6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 Jackpot = profit of: $49,999,999

5 #'s = profit of $199,999


4 & powerball =  $9,999

4 #'s = $99

3 & poswerball = $99

3 #'s = 6

2 & power ball = $6

2 #'s = loss of $1

1 & powerball = $3

1 # = loss of $1

0 # = loss of $1

(Winnings - $1ticket - taxes = Net Profit) 

Subtract the $1 spent to get total profit, but I do not know the exact taxes that come off of your profits.  I thought you actually only get about 50% of your winnings.

From wHolt - 12/10/06 10:02 AM

Pringle - If there are 146107962 ways to play and only 1 way to win,
then there are 146107961 ways to lose.
So the odds are 146107961:1, not 146107962:1
The probability is 1/146107962.
This assumes your counts are right.

From Pringle - 12/10/06 9:43 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   3478761 55*54*53*52*51/5*4*3*2*1(5*4*3*2*1 ways to pick same numbers just in different orders)
2. How many ways can you pick a Powerball number?  42 You can only pick one number out of 42
3. How many ways can you choose all 5 numbers and a Powerball number?   146107962 3478761 ways to pick 5 numbers and 42 ways to pick a powerball number. So 3478761*42
4. How many ways can you win the Jackpot?   1 You have to match all 5 numbers and the power ball number. This is only one way.
5. What are your chances of winning the Jackpot?  1/146107962 There are 146107962 ways to pick 5 numbers and a power ball number but only one way ( which has all the right numbers) can win the jackpot.
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 I will lose

66 cents

 0.0000000068(which is product of 1 /146107962)*($1* $50000000)+ (0.9999999932*-($1)) = -0.6599999932

I have 0.00000068% to win when I put one dollar and 99.99999932% to lose. 

From TBird - 12/4/06 1:50 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417451320 55*54*53..../50*49*48...
2. How many ways can you pick a Powerball number?  42 42/1=42
3. How many ways can you choose all 5 numbers and a Powerball number?   17532955440000000000(55*54*53..../50*49*48...)*42 
4. How many ways can you win the Jackpot?   1 You must match all five numbers and the powerball number to win. There is only one jackpot.
5. What are your chances of winning the Jackpot?  17532955440000000000 to 1 17532955440000000000/1
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 
IF YOU MATCHYOU WIN Profit
5 of 5 + POWERBALL JACKPOT $49,999,999
5 of 5 $200,000 $199,999
4 of 5 + POWERBALL$10,000  $9,999
4 of 5$100  $99
3 of 5 + POWERBALL $100  $99
3 of 5 $7  $6
2 of 5 + POWERBALL $7  $6
1 of 5 + POWERBALL $4  $3
POWERBALL ONLY$3 $2
 No matches $0 $-1
 Winnings

From Kathi - 12/4/06 5:15 AM

QUESTIONSANSWERSHOW?

1. How many ways
can you pick 5 #'s
of the 55 choices?

 3478761

55 possibilities for the 1st #, 54
possibilities for the 2nd #, 53 for
the 3rd #, 52 for the 4th #, and
51 for the 5th #.
55 * 54 * 53 * 52 * 51/(5*4*3*2*1)

2. How many ways
can you pick a
Powerball number?

  42 only one choice from 42 numbers

3. How many ways
can you choose all 5 #'s
& a Powerball #?  

 146,107,962

 Each combination of numbers
can have a different powerball,
so you need to multiply 3,478,761
by 42 powerball choices.

3,478,761*42 =146,107,962

4. How many ways
can you win the Jackpot?  

1

 In order to win the jackpot you
have to match all of your 5
choices and the powerball.

5. What are your
chances of winning
the Jackpot?

 146,107,962: 1

 Take all the possible
combinations of #'s
against your one
chance at winning.

 146,107,962 to 1

6. Expected profits
or losses.

  probability * profit = expected value
 Jackpot
 

1/146,107,962 = .00000000684
value = $50,000,000 * .00000000684 = .34

 

From Cheana - 12/1/06 10:55 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417451320 55*54*53*52*51=
2. How many ways can you pick a Powerball number?  42 There are 42 given numbers and only number to be picked. 
3. How many ways can you choose all 5 numbers and a Powerball number?   17532955440

 For one arrangement of "5 numbers" there are 42 different ways to choose a Powerball number, therefore, you need to multiply the number of possible arrangements for the 55 choices by 42.

42*417451320

4. How many ways can you win the Jackpot?  1 By choosing all 5 correct numbers as well as the correct Powerball number...
5. What are your chances of winning the Jackpot?  5.7035449808911394803613326242504e-11

 Divide the number of ways you can win the Jackpot by how many ways you can choose all 5 numbers and Powerball.

1/5.7035449808911394803613326242504e-11

6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game for the Jackpot. 		 $49,999,999 gain (if I win)

 Simply subtract $1 from the Jackpot of $50,000,000.

50,000,000-1=

From wHolt - 12/1/06 5:46 PM

On #6 , you only need to figure profit for the Jackpot.
Dont work so hard!

From Kathi - 12/1/06 3:40 PM

QUESTIONSANSWERSHOW?

1. How many ways
can you pick 5 #'s
of the 55 choices?

 3478761

55 possibilities for the 1st #, 54
possibilities for the 2nd #, 53 for
the 3rd #, 52 for the 4th #, and
51 for the 5th #.
55 * 54 * 53 * 52 * 51/(5*4*3*2*1)

2. How many ways
can you pick a
Powerball number?

  42 only one choice from 42 numbers

3. How many ways
can you choose all 5 #'s
& a Powerball #?  

 146,107,962

 Each combination of numbers
can have a different powerball,
so you need to multiply 3,478,761
by 42 powerball choices.

3,478,761*42 =146,107,962

4. How many ways
can you win the Jackpot?  

1

 In order to win the jackpot you
have to match all of your 5
choices and the powerball.

5. What are your
chances of winning
the Jackpot?

 146,107,962: 1

 Take all the possible
combinations of #'s
against your one
chance at winning.

 146,107,962 to 1

6. Expected profits
or losses.

  probability * profit = expected value
 Jackpot
 

1/146,107,962 = .00000000684
value = $50,000,000 * .00000000684 = .34

 5 numbers 

1/3478761 = .000000287
$200,000 * .000000287 = .057

 4 numbers +
powerball

(55*54*53*52)/(4*3*2*1) = 341055 * 42 = 14324310
1/14324310 = .000000070
$10,000 * .000000070 = .00070
 4 numbers 1/341055 = .0000029
100 * .0000029 = .00029 

3 numbers &
powerball

(55*54*53)/(3*2*1) = 26235 * 42 = 1101870
1/1101870 = .000000908
100 *  .000000908 = .0000908
 3 numbers

 1/26235 = .000038
$7 * .000038 = .00027 

 2 numbers &
powerball

 (55*54)/(2*1) = 1485 *42 = 62370
1/62370 = .0000160
$7 * .0000160 = .000112

 1 numbers &
powerball

 (55)/(1) = 55 *42 = 2310
1/2310 = .000433
$4 * .000433 = .00173
 only powerball

 1/42 = .024
$3 * .024 = .071 

 

From Fro - 11/30/06 9:03 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   3,478,761(55*54*53*52*51) / (5*4*3*2*1).
2. How many ways can you pick a Powerball number?  4242 *1 = 42.
3. How many ways can you choose all 5 numbers and a Powerball number?   146,107,9623,478,761*42 = 146,107,962.
4. How many ways can you win the Jackpot?   1There is only one way to win the Jackpot. 
5. What are your chances of winning the Jackpot?  1:146,107,962 There is only 1 way out of 146,107,962 chances.
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 $49,999,999 or
- $1		 A winning ticket would net $49,999,999 profit. A losing ticket would result in a $1 loss.

From Draco - 11/28/06 6:05 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   3478761 55*54*53..../(50*49*48...)*(5*4*3*2*1)
2. How many ways can you pick a Powerball number?  42 42/1=42
3. How many ways can you choose all 5 numbers and a Powerball number?   146107962(55*54*53..../(50*49*48...)*(5*4*3*2*1)*42 
4. How many ways can you win the Jackpot?   1 You must match all five numbers and the powerball number to win. There is only one jackpot.
5. What are your chances of winning the Jackpot?  146107962 to 1 146107962/1
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 
IF YOU MATCHYOU WIN Profit
5 of 5 + POWERBALL JACKPOT $49,999,999
5 of 5 $200,000 $199,999
4 of 5 + POWERBALL$10,000  $9,999
4 of 5$100  $99
3 of 5 + POWERBALL $100  $99
3 of 5 $7  $6
2 of 5 + POWERBALL $7  $6
1 of 5 + POWERBALL $4  $3
POWERBALL ONLY$3 $2
 No matches $0 $-1
 Winnings-$1

From wHolt - 11/28/06 10:20 AM

DirtyBird & All -
Some of you are copying the guy just above you,
but some of you are actually thinking and coming up with good ideas.
If I were you, I would be reading everyone's answers,
and deciding which were better than others.
What I want you to experience in this course is actually the way making decisions is like in "real" life.
In real life, we have no authority telling us what is right,
or we have so many authorities we cannot believe any of them,
unless we blindly choose someone to believe.
But there is something unAmerican about letting someone else
continuously make our decisions for us.
That's why we have such courses as these.
You can do it
because those of you who have made it this far have proven that your brain works.
My job is to encourage you to exercise it.
Patience...

From DirtyBird - 11/27/06 6:46 PM

Mr. Holt, I dont believe that anyone understands what you are saying about #6 since everybody is still doing it the same way. If you could shead a little more light on it that would be nice. Thanks.

From wHolt - 11/27/06 9:46 AM

Melewen - are you counting the order of picking, or not?

From Melewen - 11/26/06 11:15 PM

QUESTIONS ANSWERS HOW? 
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?
3478761 Since order matters, you take the total combination of all the 55 numbers (55x54x53x52x51). Then you
divide that by all the possibilities of duplicates (5x4x3x2x1). So, (55x54x53x52x51)/(5x4x3x2x1).
2. How many ways can you pick a Powerball number?
 42Since there are 42 options and you get to pick only one, there is naturally 42 ways to pick a Powerball number.
3. How many ways can you choose all 5 numbers and a Powerball number?
146107962  You multiply the number of ways to pick 5 numbers from 55 (3478761) by the Powerball number options (42).
4. How many ways can you win the Jackpot?  
 1 You have to have all the right numbers, so naturally there is only one way to win the jackpot.
5. What are your chances of winning the Jackpot?  
 .000000006 1/146107962
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game for the Jackpot.
Expected loss: $ .999999994
Expected gain:
$ .000000006
 You multiply the chance of winning (.000000006) by $1, which is $ .000000006. Then you subtract that from $1 to find the average, probably earnings, which makes .999999994

 

From wHolt - 11/26/06 7:48 AM

David -
if you are expressing odds, write 1:146107961
when expressing probability, write 1/146107962

on #6, compute only your expected gain or loss for the Jackpot.
forget the little pots. keep it simple somewhat...

From SuperDuke - 11/26/06 12:18 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?  3,478,761 5 different numbers of 55 (55x54x53x52x51) divided by the possible orders of arrangement those #'s (5x4x3x2x1)                                                                                      
2. How many ways can you pick a Powerball number?  42 There are 42 possible numbers which is 1:42
3. How many ways can you choose all 5 numbers and a Powerball number?   146,107,9623,478,761 ways to pick the 5 and then 42 ways to pick the powerball. so it would be 3,478,761 x 42
4. How many ways can you win the Jackpot?   120 ways although you must have the correct 5 numbers plus the power ball, there are 120 number varitions that will win. The 5 numbers do not have to be in order and there are 120 different orders they can be in (5x4x3x2x1). So there are 120 different ways to have the winning ticket.
5. What are your chances of winning the Jackpot?  1n:146,107,962 n= # of dollars spent
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 an expected gain of 34 cents and a loss of 66 cents  (%chance of win * Amount of win = .34221269) + (%chance of loss * loss =  -.99999999) = -.6577873

I can change the terms a little and make it easier to understand #6 . If the odds of winning were 1 in 150 million, and the jackpot was 50 million. You would have to buy 150 million tickets (with different #'s) in order to garrantee the return of 50 million. thats a gain of 1/3 and loss of 2/3. so for every dollar you spend you will gain 33 cents and lose 67 cents.

 

From David - 11/25/06 9:04 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?  3478761remembering almagrams, and since there is only one of each numbered ball in the spinning thing, the equasion is (55*54*53*52*51)/(5*4*3*2*1)
2. How many ways can you pick a Powerball number? 42 Only one way to pick one number from 42 numbers 
3. How many ways can you choose all 5 numbers and a Powerball number?  146107962  multiply 3478761*42 (I assume this bears no repeating)
4. How many ways can you win the Jackpot?  1 only one way to win out of the 146107962 options 
5. What are your chances of winning the Jackpot? 1:146107962 not good.
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 -8.33168

 I dont know if I completely understand how to use the equation that WHolt gave us but it goes something like this-

.00000000684(50000000*1)+.00000028(200000*1)+.00000171(10000*1)+.0000701(100*1)+.0000838(100*1)+.00343(7*1)+.00134(7*1)+.00787(4*1)+.0144(3*1)+.999(-1)+.999(-1)+.999(-1)+.999(-1)+.999(-1)+.996(-1)+.998(-1)+.992(-1)+.985(-1)= -8.33168

the .00000000684 represents the chance that you will win the jackpot, the .00000028 represents the chance that you will win the $200000 and so on....

....The .999 and so on represents the chance that you will loose.

 This tells me that the Tennessee lottery should be paying us to play the game..........or something.

 

From Zonino - 11/23/06 11:19 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   3,478,761 We want to pick 5 numbers out of 55.  This would be 55*54*53*52*51.  However, like the Amalgam problem, we want to remove all of the duplications ( 1 2 3 4 5 for example is the same as selecting 5 4 3 2 1).  Thus we would have (55*54*53*52*51) / (5*4*3*2*1).  This is 417,451,320 / 120 or 3,478,761
2. How many ways can you pick a Powerball number?  42 There are 42 options and you are selecting one number.  42 options *1 pick = 42.
3. How many ways can you choose all 5 numbers and a Powerball number?   146,107,962 Since you pick the two numbers separately and they are unrelated, you would simply multiple the two numbers together to find the total number of ways you can choose both the 5 numbers and the powerball.  This is 3,478,761*42 or 146,107,962.
4. How many ways can you win the Jackpot?   1 There is only one way to win the Jackpot.  You must select the 5 numbers and the Powerball.  The 5 numbers order does not matter, thus the reason why there is only 1 way and not 5*4*3*2*1 ways to pick the correct numbers.  There is only 1 correct powerball.  So thus we have 1*1= 1 ways.
5. What are your chances of winning the Jackpot?  1:146,107,962 There is only 1 way out of 146,107,962 possibilities of winning the Jackpot.
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		  Still working on this one...  it is a bit tricky.

 

From Draco - 11/23/06 8:32 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417451320 55*54*53..../50*49*48...
2. How many ways can you pick a Powerball number?  42 42/1=42
3. How many ways can you choose all 5 numbers and a Powerball number?   17532955440000000000(55*54*53..../50*49*48...)*42 
4. How many ways can you win the Jackpot?   1 You must match all five numbers and the powerball number to win. There is only one jackpot.
5. What are your chances of winning the Jackpot?  17532955440000000000 to 1 17532955440000000000/1
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 
IF YOU MATCHYOU WIN Profit
5 of 5 + POWERBALL JACKPOT $49,999,999
5 of 5 $200,000 $199,999
4 of 5 + POWERBALL$10,000  $9,999
4 of 5$100  $99
3 of 5 + POWERBALL $100  $99
3 of 5 $7  $6
2 of 5 + POWERBALL $7  $6
1 of 5 + POWERBALL $4  $3
POWERBALL ONLY$3 $2
 No matches $0 $-1
 Winnings-$1

From Taurus - 11/23/06 5:21 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417451320 55*54*53*52*51=417451320
2. How many ways can you pick a Powerball number?  42 42 options, 1 pick.
3. How many ways can you choose all 5 numbers and a Powerball number?   17532955440 42*417451320
4. How many ways can you win the Jackpot?   1 Only 1 way to win because there is only one way to match a all the numbers.
5. What are your chances of winning the Jackpot?

 .000000000057

1/17532955440

 1/17532955440
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 $1 loss with only one purchase

 You lose only invested materials.

From Capricorn - 11/23/06 5:01 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417451320 55*54*53*52*51=417451320
2. How many ways can you pick a Powerball number?  42 42 options, 1 pick.
3. How many ways can you choose all 5 numbers and a Powerball number?   17532955440 42*417451320
4. How many ways can you win the Jackpot?   1 A jackpot is every number matched, only one way to pick it out.
5. What are your chances of winning the Jackpot?  .000000000057 1/17532955440
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 $1 loss

 You can only lose what you put in. You gain all but what you put in.

From CenterField - 11/23/06 1:39 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417,451,32055*54*53*52*51; No order distinction; cannot choose any number more than once.
2. How many ways can you pick a Powerball number?  42The number of ways you can pick 1 number from 42 choices.
3. How many ways can you choose all 5 numbers and a Powerball number?   17,532,955,440(Answer #1)*(Answer #2) = 417,451,320*42
4. How many ways can you win the Jackpot?   1 Order does not matter, and there are no duplicates. Multiple people may win, but there is only one correct combination.
5. What are your chances of winning the Jackpot? 1:17532955440 or 5.70E-12There is one correct answer out 17,532,955,440 possible answers; in other words, odds are slim to almost none.
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 Profits: $49,999,999

Losses: $1

 Subtract your investment from your winnings; If you win: $50m-$1, or, if you lose, $0-$1= -$1

 

From wHolt - 11/23/06 11:05 AM

It is highly recomended that everyone read previous answers before you randomly copy.

From Tiger - 11/23/06 10:49 AM

 Questions                      Answers            How?                                 
 1. How many ways can you pick 5 numbers out of 55 choices on the ticket? 417,451,320 55*54*53*52*51=417,451,320
 2. How many ways can you pick a powerball number? 42 There are 42 choices and you can only pick 1. 42*1=42
 3. How many ways can you chose all 5 numbers and a powerball number? 17,532,955,440 Total ways you can chose 5 numbers times the number of ways to chose a powerball number. 417,451,320*42= 17,532,955,440
 4. How many ways can you win the jackpot? 1 All 5 numbers and powerball have to match.
 5. What are your chances of winning the jackpot? .000000000057

 Your 1 ticket divided by the total number of ways possible. 1/17,532,955,440

 6. If it costs $1 to play one powerball game, and the jackpot is $50 million, predict your expected profits or losses in playing one game. 49,999,999:1 $50 million minus my one dollar ticket would be my profit. My loss would be a dollar.

From 7Iron - 11/23/06 10:24 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   0.0909 5/55
2. How many ways can you pick a Powerball number?  .0238095 1/42
3. How many ways can you choose all 5 numbers and a Powerball number?   146,107,962 ((55*54*53...)/(5*4*3...)*(50*49*48...))*((42*41*40...)/(1)*(41*39*38...))
4. How many ways can you win the Jackpot?   8.19*10^-117 
(previous how) / ((55*54*53...)*(42*41*40...))
5. What are your chances of winning the Jackpot?  6.844254*10^-9 1/(146107962)
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 profits 0

losses 1

 look at the chances, it is practically impossible!! 

 

I am going to stop playing!!

From BassLady - 11/23/06 12:09 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417,451,31055*54*53*52*51 
2. How many ways can you pick a Powerball number?   
3. How many ways can you choose all 5 numbers and a Powerball number?    
4. How many ways can you win the Jackpot?   1 You must have the 5 numbers correct along with the powerball number
5. What are your chances of winning the Jackpot?  1 out of 146,107,962The Tennessee lottery website states this is the odds
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 49,499,999 I win $50 million and I win by paying $1.  I don't accept the "all at one time" payout.  I choose the payment plan.  Of course this is not counting the IRS payment for taxes.

From Pringle - 11/22/06 3:49 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417451320 55*54*53*52*51 order doesn't matter so I didn't divide this by 5*4*3*2*1
2. How many ways can you pick a Powerball number?  42 You can only pick one number out of 42
3. How many ways can you choose all 5 numbers and a Powerball number?   17532955440 417451320 ways to pick 5 numbers and 42 ways to pick a powerball number. So 417451320*42
4. How many ways can you win the Jackpot?   1 You have to match all 5 numbers and the power ball number. This is only one way.
5. What are your chances of winning the Jackpot?  17532955440:1 There are 17532955440 ways to pick 5 numbers and a power ball number but only one way ( which has all the right numbers) can win the jackpot.
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 I will lose

$.99997149999943

 0.000000000057(which is product of 17532955440:1)*($1* $50000000)-99.999999999943*$1

I have 0.0000000057% to win when I put one dollar and 99.9999999943% to lose. 

 

From wHolt - 11/22/06 1:41 PM

Read each others comments.
Decide who you agree with and why.
Maybe no one is correct.
Does anyone know how to subtract loss from profit to find net?

From Harkar - 11/21/06 7:42 PM

QUESTIONS
ANSWERS
HOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?  
 3,478,761
55*54*53*52*51/5*4*3*2*1
 order doesn’t matter.
2. How many ways can you pick a Powerball number?
 42
 1 choice out of 42 numbers
3. How many ways can you choose all 5 numbers and a Powerball number?  
 146,107,962
3,478,761 * 42 = 146,107,962
4. How many ways can you win the Jackpot?  
120 ways
Even though you have to have the correct 5 numbers plus the power ball, there are still 120 different variations that will win. The 5 numbers do not have to be in order so: 5*4*3*2*1= 120.
5. What are your chances of winning the Jackpot?
 1:146,107,962
 Ways wanted = 1
Ways total = 146,107,962
So:  1/146,107,962
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.
 Potential Loss = $1
Potential Profit, if win = $49,999,999
 Potential Profit = $50,000,000 minus $1 = $49,999,999

From GolfGirl - 11/21/06 4:38 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   3,478,761 55*54*53*52*51/(5*4*3*2*1
2. How many ways can you pick a Powerball number?  42 C=(42,1)
3. How many ways can you choose all 5 numbers and a Powerball number?   146,107,962 3,478,761*42
4. How many ways can you win the Jackpot?   10,593,800

 (5*4*3*2*1)/1*4*3*2*1=120/24=5

55-5=50 no win

C(50,5)

(50*49*48*47*46)(5*4*3*2*1= 2,118,760

5*2118760=10,593,800 ways to win

5. What are your chances of winning the Jackpot?  .000000019

 37*36*35*34*33=52307640

1/52307640

6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 loss I always lose!!

From wHolt - 11/21/06 12:58 PM

Question #6 requires you to weigh your profit and losses.
If you buy a stock that has a 60% chance of doubling in value
and a 40% chance of bankrupting,
and you invest $1000 in it,
how do you compute your profit and/or loss?
In other words, what is the expected value of your investment?

Expected Value = .60(2*1000) + .40(-1000) = 1200 - 400 = $800

From DirtyBird - 11/20/06 8:37 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417,451,320

5 numbers out of 55 numbers. Order doesn't matter.

55*54*53*52*51=417,451,320 

2. How many ways can you pick a Powerball number?  42You have 1 pick and you can select any of the 42 numbers. 
3. How many ways can you choose all 5 numbers and a Powerball number?   17,532,955,440You have 417,451,320 ways to pick 5 numbers times your 42 ways to get the power ball number. 417,451,320*42=17,532,955,444 
4. How many ways can you win the Jackpot?  1  You must have all 5 numbers along with the 1 powerball number right. Thant will give you 1 shot at the big bucks.
5. What are your chances of winning the Jackpot?  1:17,532,955,440All possibilities of the combinations for your 1 chance.
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 
 5 of 5+POWERBALL JACKPOT49,999,999 
 5 OF 5

200,000

199,999 
 4 OF 5+POWERBALL10,000 9,999 
 4 OF 5100 99 
 3 OF 5 +POWERBALL100 99 
 3 OF 5 76
 2 OF 5+POWERBALL7 6 
 1 OF 5+POWERBALL4 3 
 POWERBALL ONLY3 2 
 You have to take out $1 you spent on the ticket that you bought to get your true earnings.(Minus taxes also if you win)

 

From Houdini - 11/20/06 1:06 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417,451,320Five numbers out of fifty five, order does not matter, 55x54x53x52x51
2. How many ways can you pick a Powerball number?  42 One choice out of 42 numbers.
3. How many ways can you choose all 5 numbers and a Powerball number?   17,532,955,440 417451320 ways to choose five numbers out of 55 multiplied by 42 ways to choose one number out of 42.
4. How many ways can you win the Jackpot?   1 you must match all 5 numbers plus the powerball to win the jackpot, therefore there is only one way to win.
5. What are your chances of winning the Jackpot?  17,532,955,440:1There are 17,532,955,440 ways to choose your numbers against one way to win the jackpot. 
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 
5 of 5 + POWERBALL JACKPOT $49,999,999
5 of 5 $200,000 $199,999
4 of 5 + POWERBALL$10,000  $9,999
4 of 5$100  $99
3 of 5 + POWERBALL $100  $99
3 of 5 $7  $6
2 of 5 + POWERBALL $7  $6
1 of 5 + POWERBALL $4  $3
POWERBALL ONLY$3 $2
 Odds 

5 of 5 + POWERBALL 

17,532,955,440:1
5 of 5 417,451,320:1
4 of 5 + POWERBALL343,783,440:1
4 of 58,185,320:1
3 of 5 + POWERBALL 6,611,220:1
3 of 5 157,410:1
2 of 5 + POWERBALL 124,740:1
1 of 5 + POWERBALL  2310:1
POWERBALL ONLY42:1

From wHolt - 11/20/06 11:21 AM

Ask yourself this question when deciding to count order or no order:
Will the number be larger or smaller one way or the other?

From Kathi - 11/20/06 7:33 AM

I didn't take into consideration that the numbers were not in any order.

 

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   3478761

55 possibilities for the first, 54 possibilities for the second, 53 for the third, 52 for the fourth, and 51 for the fifth number drawn.
55 * 54 * 53 * 52 * 51/(5*4*3*2*1)

2. How many ways can you pick a Powerball number?   42 only one choice from 42 numbers
3. How many ways can you choose all 5 numbers and a Powerball number?   146,107,962

 Each combination of numbers can have a different powerball, so you need to multiply 3,478,761 by 42 powerball choices.

3,478,761*42 =146,107,962

4. How many ways can you win the Jackpot?  1

 In order to win the jackpot you have to match all of your 5 choices and the powerball. This allows that each of your numbers must be an exact match. Because of this you can only win the Jackpot in one way: match all numbers.


5. What are your chances of winning the Jackpot?  146,107,962: 1  Take all the possible combinations of numbers against your one chance at winning.

 146,107,962 to 1

6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 Jackpot = profit of: $49,999,999

5 #'s = profit of $199,999


4 & powerball =  $9,999

4 #'s = $99

3 & poswerball = $99

3 #'s = 6

2 & power ball = $6

2 #'s = loss of $1

1 & powerball = $3

1 # = loss of $1

no matches loss of $1

 You have to subtract the $1 spent to get true profit.

 

From Houdini - 11/20/06 12:54 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417451320 55x54x53x52x51
2. How many ways can you pick a Powerball number?  42 1 choice of 42 numbers
3. How many ways can you choose all 5 numbers and a Powerball number?    
4. How many ways can you win the Jackpot?    
5. What are your chances of winning the Jackpot?   
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		  

From Boki - 11/18/06 4:58 PM

I prefer this way 55 * 54 * 53 * 52 * 51/(5*4*3*2*1) because the order of these 5 white balls does not count.

55 * 54 * 53 * 52 * 51 is the number of ways to choose 5 numbers in order.

From wHolt - 11/18/06 1:40 PM

Some of you are answering #1 as 55 * 54 * 53 * 52 * 51/(5*4*3*2*1)
and some are saying it should be 55 * 54 * 53 * 52 * 51.
Tell us why you prefer one way or the other.

From Boki - 11/18/06 12:00 AM

QUESTIONS
ANSWERS
HOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?  
 3478761
There are 55 possibilities for the first, 54 possibilities for the second, 53 for the third, 52 for the fourth, and 51 for the fifth number drawn.
 55 * 54 * 53 * 52 * 51/(5*4*3*2*1)
2. How many ways can you pick a Powerball number?
           42
 (42*41*40*39*38)/ (5*4*3*2*1)= 850668
Since the Powerball number is chosen from 42 numbers, to choose 1 of them we will have C(42,1)=42 possibilities.

3. How many ways can you choose all 5 numbers and a Powerball number?  
 146,107,962
 It will be a product of these two above:
3,478,761*42 =146,107,962
4. How many ways can you win the Jackpot?  
 10593800
 Jackpot  means all five winning numbers selected, and we will have (5*4*3*2*1)/1*(4*3*2*1)=120/24=5 ways to select one winning number out of 5 winning numbers.
Then we have 55-5=50 numbers that don’t win. So there are C(50,5) = =(50*49*48*47*46)/ (5*4*3*2*1) = 2 118 760 ways to select 5 out of 50 numbers that don't win.
Total: 5*2 118 760=10593800 ways to select 5 out of 55 numbers, with one that is a winning number.

5. What are your chances of winning the Jackpot?
 .000000019
Here we need Powerball total of equally likely combinations of not-wining numbers (after 5 winning numbers have been excluded) which are (37*36*35*34*33) = 52307640.
Since the number of ways that Powerball number can match the single Powerball number is C(1,1) = 1 and the number of ways that Powerball number can match all 5 Powerball number is C(5,5) = 1,
the product C (5,5) x C (1,1) = 1 is the number of ways you can win the Jackpot .
So, my chance to win the Jackpot will be 1/ 52307640 =.000000019
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.
 

Matches,

 nine ways to win
Prize ($)
Probability
  1. HOW?
  2.  Expected Value
5+1
jackpot
$50.000.000
to win is
.0000000068

1. C(55,5)=(55*54*53*52*51)/5*4*3*2*1=3478761

C1(42,1)=42

C(55,5)* C1(42,1)= 3478761*42=146 107 962

P(C)=1/3478761=.000000287

P(C)=1/42=.023809523

P(C and C1)=1/146 107 962=.0000000068
2.
Expected Value:
$50 000 000*.0000000068= $0.34
5
$ 200,000

to win is
 .000000287

1. C(55,5)=(55*54*53*52*51)/5*4*3*2*1=3478761

P(C)=1/3478761=.000000287

2.
Expected Value:
$ 200,000 *0.000000287=$0.05603330

4 + 1
$ 10,000

to win is
0.0000000698

1. C(55,4)=(55*54*53*52)/ 4*3*2*1=341 055
C1(42,1)=42   

P(C)=1/341 055=.000002932P(C1)=1/42=.023809523
P(C and C1)= .000002932*.023809523=0.0000000698
2.
Expected value:
$ 10,000 * 0.0000000698=0.000698
or 0.0698 cents per $1

4
$ 100

to win is
 0.000002862

1. C(55,4)=(55*54*53*52)/ 4*3*2*1=341 055

P(C)=1/341 055=.000002932

2. Expected value:
$ 100 *0.000002932=$0.0002862
3 + 1
$ 100

to win is
0.000000907

1. C(55,3)=(55*54*53)/ 3*2*1=26 235
C1(42,1)=1/42   

P(C)=1/26 235=.000038117

P(C1)=1/42=0.023809523
P(C and C1)= .000038117*.023809523= 0.000000907
2. Expected value:
$ 100 *0.000000907=$0.0000907
3 
$ 7

to win is
0.000037209

1. C(55,3)=(55*54*53)/ 3*2*1=26 235

P(C)=1/26 235=.000037209

2. Expected value:
$ 7 *0.000037209=$0.00026
2 + 1
$ 7

to win is
0.00016033

1. C(55,2)=(55*54)/ 2*1=1 485
C1(42,1)=1/42

P(C)=1/1 485=.0006734

P(C1)=1/42=0.023809523
P(C and C1)= .0006734*0.023809523=.00016
2. Expected value:
$ 7 *.00016=$0.00112
1 + 1
$ 4

to win 0.00043

1. C(55,1)=55
C1(42,1)=1/42

P(C)=1/55=.0181818

P(C1)=1/42=0.023809523
P(C and C1)= .0181818*0.023809523=0.00043
2. Expected value:
$ 4 *0.00043=$0.0017
0 + 1
$ 3

to win is
0.023809523
 1.
C1(42,1)=1/42
P(C1)=1/42=0.023809523
2. Expected value:
$0.071428569
Total
$50 210 221
to win is
0.242621776
Or 24.26%

Total expected value:

$50 210 221*0.082786829= $12 362 648
Expected Value

$50 210 221

of loss.7574
or 75.74%
$50 210 221*.7574=$38 029 221.39
p(win)/p(loss)= 0.242621776/.7574=0.32034
or 32%
which means that profit/loss ratio is 1 to 32

From wHolt - 11/17/06 2:56 PM

Do not forget all your counting techniques you have previously learned!

From Trixie - 11/16/06 6:40 PM

QUESTIONSANSWERS HOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417,451,320  Using the same counting technique as in the other assignments, I used 55*54*53*52*51 = 417,451,320
2. How many ways can you pick a Powerball number?

 42

  You can pick any number between 1-42. That means you have 42 different ways to pick a powerball number.
3. How many ways can you choose all 5 numbers and a Powerball number?  

 17,532,955,440

  Multiply, your total number of ways to pick 5 out of 55 numbers (417,451,320), by , your total number of ways to pick a powerball number (42). 417,451,320 * 42 =17,532,955,440 total possible ways
4. How many ways can you win the Jackpot?  

 1

  In order to win the jackpot, you have to have the exact same 5 numbers (in any order) and the exact same powerball number. So there is only one way to win the jackpot.
5. What are your chances of winning the Jackpot?

 

  
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		   

From Sunshine - 11/16/06 2:16 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   
3478761

 COMBIN(55,5)= COMBINATIONS OF 55 ITEMS TAKEN 5 AT A TIME.

2. How many ways can you pick a Powerball number?  42 COMBIN(42,1) = COMBINATIONS OF 42 ITEMS TAKE 1 AT A TIME.
3. How many ways can you choose all 5 numbers and a Powerball number?  146,107,962 3,478,761 X 42
4. How many ways can you win the Jackpot?   1 WAY ALL 5 PLUS POWERBALL MUST MATCH
5. What are your chances of winning the Jackpot?  .000000006 1/146107962
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 
 5 of 5+POWERBALL JACKPOT49,999,999 
 5 OF 5

200,000

199,999 
 4 OF 5+POWERBALL10,000 9,999 
 4 OF 5100 99 
 3 OF 5 +POWERBALL100 99 
 3 OF 5 76
 2 OF 5+POWERBALL7 6 
 1 OF 5+POWERBALL4 3 
 POWERBALL ONLY3 2 
49999999		 subtract $1 from the Jackpot of $50,000,000.

 

From wHolt - 11/15/06 2:08 PM

Ideas to check:
Does the order in which you pick your 5 numbers matter?
Can you pick the number 7 more than once?

From Kathi - 11/15/06 9:01 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417,451,320

55*54*53*52*51= 417,451,320

2. How many ways can you pick a Powerball number?  42

 1 way of 42 choices:  42 

3. How many ways can you choose all 5 numbers and a Powerball number?   17,532,955,440

 you have 417,451,320 ways to pick 5 numbers and 42 ways to choose a power ball for each of those choices

417,451,320 * 42 = 17,532,955,440 

4. How many ways can you win the Jackpot?   1 In order to win the jackpot you have to match all of your 5 choices and the powerball. This allows that each of your numbers must be an exact match. Because of this you can only win the Jackpot in one way: match all numbers.
5. What are your chances of winning the Jackpot?  17,532,955,439 : 1

 Take all the possible combinations of numbers against your one chance at winning.

17,532,955,439 to 1

6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game.

 Jackpot = profit of: $49,999,999

5 #'s = profit of $199,999

4 & powerball =  $9,999

4 #'s = $99

3 & poswerball = $99

3 #'s = 6

2 & power ball = $6

2 #'s = loss of $1

1 & powerball = $3

1 # = loss of $1

no matches loss of $1 

 You have to subtract the $1 spent to get true profit.

From Pac - 11/14/06 5:39 PM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   417,451,320 55*54*53*52*51 = 417,451,320
2. How many ways can you pick a Powerball number?  42 There are 42 options and you only pick 1 number.
3. How many ways can you choose all 5 numbers and a Powerball number?   17,532,955,440 417,451,320 * 42 because you have one Powerball option for each of the other 5 numbers chosen
4. How many ways can you win the Jackpot?   1 You have to match all five numbers AND the Powerball, so there is only one way.
5. What are your chances of winning the Jackpot?  0.000000000057 1 / 17,532,955,440 (ways wanted divided by ways total)
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		 I'd predict that I'd lose my $1. No math, I just always lose.

Revised 11/19

From wHolt - 11/13/06 10:22 AM

Kathi - use the counting techniques learned in the previous assignments
to count the ways to choose 5 things out of 55.

From Kathi - 11/13/06 5:13 AM

QUESTIONSANSWERSHOW?
1. How many ways can you pick 5 numbers out of the 55 choices on the ticket?   .0909

 5 ways of 55 choices:

5/55 = .090 

2. How many ways can you pick a Powerball number?  .0238

 1 way of 42 choices:

1/42 = .0238 

3. How many ways can you choose all 5 numbers and a Powerball number?    
4. How many ways can you win the Jackpot?    
5. What are your chances of winning the Jackpot?   
6. If it costs $1 to play one Powerball game, and the Jackpot is $50 million,
predict your expected profits or losses in playing one game. 		  



Last Modified 11/27/06 9:48 AM

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