Question
Asked Feb 22, 2019
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27. Game of Craps In a game of craps, a player wins on
the first roll if the player rolls a sum of 7 or 11, and the
player loses if the player rolls a 2, 3, or 12. Find the
probability that the game will last only one roll.
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27. Game of Craps In a game of craps, a player wins on the first roll if the player rolls a sum of 7 or 11, and the player loses if the player rolls a 2, 3, or 12. Find the probability that the game will last only one roll.

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Expert Answer

Step 1

Given a player wins if he rolls a sum of 7 or 11 when rolled a pair of dice.

A player loses if he rolls a sum of 2, 3 or 12.

We need t find the probability that game will last only one roll. So here we need to find the probability of either win or loss in first roll, such that game will last only one roll.

If two events A,B are mutually exclusive then we can say that both events does not occur simultaneously. So P(A or B) = P(A) + P(B). Here win and loss are both mutually exclusive events. So we can say

P(Win or loss) = P(win)+P(loss)

Step 2

P(Win) = probability of rolling 7 or 11.

When a die is rolled number of possibilities = 6

When two dice are rolled, number of possibilities = 6*6 = 36.

The total number of ways of rolling a 7 when we roll two dice = 6 ways(as shown below)

The total number of ways of rolling a 11 when we roll two dice = 2 ways...

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