Questions A and B

Question

A. What are the odds for rolling a sum of 9 in a single roll of two fair dice? (Simplify answer in a fraction)

 

B. If you bet $1 that a sum of 9 will turn up, what should the house pay(plus returning your $1 dollar bet) if a sum 9 turn up for the game to be fair? (Simplify answer to the nearest cent)

Answer 1

Question A can be answered by the following analysis.

die 1 a 3, die 2 a 6

die 1 a 6, die 2 a 3

die 1 a 4, die 2 a 5

die 1 a 5, die 2 a 4

 

so, there are 4 ways to roll a 9. Since there 36 possible combinations, the chance of rolling a total of 9 on a single roll is 4 divided by 36 = 0.11 or 11%.

 

Question B cannot be calculated, as pay off is somewhat arbitrary. Currently, Las Vegas casinos pay 1 to 1 on such a bet. That pay off has been the case for a long time.

Answer 2

 

A. if you roll a pair of dice there are 36 possible outcomes (sums)

1+1=2

1+2=3

1+3=4

1+4=5

1+5=6

1+6=7

2+1=3

2+2+4

2+3=5

2+4=6

2+5=7

2+6=8

3+1=4

3+2=5

3+3=6

3+4=7

3+5=8

3+6=9

4+1=5

and so on

when you roll the dice you can get 3 on die #1 and 6 on die #2, 6 on die #1 and 3 on die #2, 4 on die #1 and 5 on die #2, and 5 on die #1 and 4 on die #2

3+6, 6+3, 4+5, and 5+4 all equal 9

the probability is 4/36, or 1/9

if you mean odds (in favor) of rolling a sum of 9 that's a little different

odds=probability event will occur/probability event will not occur

odds=4/32 (36 outcomes, 4 favorable and 32 not favorable)

odds=1/8

look at the probability answer 1/9; 1 way it can happen out of 9 ways so 8 ways it cannot happen, 1/8=odds

4/36 means 4 ways it can happen out of 36 ways so 32 ways it cannot happen

 

B. different games and different places have different percentage payouts

   do you have a formula ?