# math

posted by .

A pair of dice is rolled once. suppose you lose \$9 if the dice sum to 9 and win \$11 if the dice sum to 4 or 6. how much should you win or lose if any other number turns up in order for the game to be fair?

• math -

There are 6 combinations for the first dice, and 6 combinations for the second dice, so the total number of possibilities is 36

There are only 4 ways to get a sum of 9: (4,5), (5,4), (3, 6), (6, 3)

There are only 3 ways to get 4: (2, 2), (1,3), (3,1)

There are only 5 ways to get 6: (1,5), (5,1), (2,4), (4,2), (3,3)

So there are 8 ways to get 4 or 6

There are 36-8-4 = 24 other possible ways to get another number

For the game to be fair, the sum of all the probabilities multiplied by the gain/loss for each of them should be 0:

-\$9 *(4/36) + \$11*(8/36) + x*(24/36) = 0

solve for x

## Similar Questions

1. ### algebra

two dice are rolled. if a 3 appears on either dice,then the two dice are rolled again and the two dice are added togather. if a 3 does not appear, then we ll add the two dice togather. if the sum of two dice is even ,i win and if the …
2. ### math

suppose a pair of dice is rolled. Consider the sums of numbers on the top of the dice. Find the probabilities: a) P(5, given that the sum are odd) b) P(odd, given that the sum rolled is 5) c) P(7, given that one of the dice rolled …
3. ### math

In rolling a pair of dice, suppose you win \$5 if the sum is 10 but lose \$2 if the roll is "doubles." If the price to play is \$1, would it be a fair game?
4. ### Math

Suppose you play a game in which two fair standard dice are rolled. If the numbers showing on the dice are different, you lose \$2. If the numbers showing are the same, you win \$2 plus the dollar value of the sum of dice. Complete the …
5. ### math

a pair of dice is rolled. is the event of rolling a sum of the dice is an odd number. Find the probability that the sum is a five or a ten, given that an odd sum is rolled.
6. ### Probability and statistics

A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win \$5. If you roll a 5, 6, 7, 8, or 9 you lose \$5. Find the expected value you win (or lose) per game.
7. ### Finite Math

Bill and Fred are betting on the outcome when two fair dice are rolled. If the dice sum is any even number, other than 8, Bill pays Fred \$8. If the dice sum is 8, Bill pays Fred \$1. If the dice sum is odd, Fred pays Bill \$2. What is …
8. ### Elementary Statistics

10. In a game of “chuck a luck” three dice are rolled. If your number comes up on all three dice you win \$3. If your number comes up on two dice you win \$2. If your number comes up only once you win \$1. If your number doesn’t …
9. ### math

You play a game in which two dice are rolled. If a sum of 7 appears, you win \$10. Otherwise you lose \$2.00. If you intend to play the game for a long time should you expect to make money, lose money or come out even?
10. ### math

A pair of 6 sided fair dice are rolled. If one of the dice shows an odd number what is the probability of the sum of the dice being 7 ?

More Similar Questions