# Calculating probabilities for the dice game called "craps"

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A popular dice game, called "craps," is played in the following manner. A player starts by rolling two dice. If the result is a 7 or 11, the player wins. If the result is 2, 3, or 12, the player loses. For any other sum appearing on the dice, the player continues to roll the dice until that outcome reoccurs (in which case the player wins) or until a 7 occurs (in which case the player loses).

a) What is the probability that a player wins the game on the first roll of the dice?

b) What is the probability that a player loses the game on the first roll of the dice?

c) If the player throws a 4 on the first roll, what is the probability that the game ends on the next roll?

d) If the player throws a 4 on the first roll, what is the probability that he will eventually win the game?

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##### Solution Summary

The solution gives an intuitive approach to probability problems involving dice. The technique is illustrated by calculating probabilities for the game of "craps".

##### Solution Preview

Please see the attached Word document to view the table described in this solution.

The values 1 through 6 on the left and top margins of the table are the possible outcomes of one die. The body of the table contains the sum of the two values in the margins, the total when two dice are rolled.

There are 36 equally likely outcomes when two dice are rolled. The probability of an event when rolling a pair of dice can be determined by counting the ...

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