4 Consider the game where two dice six sided die A and die B

4. Consider the game where two dice (six sided), die A and die B, are rolled. We say die A wins, and write A>B, if the outcome of rolling is larger than that of rolling B. If both rolls result in the same number it is a tie.

a. Find the probability of a tie.

b. Find the probability that die A wins.

Solution

a)

There are 36 ways to roll two dice, and 6 ways so that it is a tie.

thus,

P(tie) = 6/36 = /16 or 0.16666667 [ANSWER]

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b)

Note that the probability that A wins is the same as the probability that B wins.

Thus,

P(A wins) + P(B wins) + P(tie) = 1

P(A wins) + P(A wins) + P(tie) = 1

2P(A wins) + P(tie) = 1

2P(A wins) + 1/6 = 1

2P(A wins) = 5/6

P(A wins) = 5/12 or 0.416666667 [ANSWER]