Consider a game where a die is rolled three times and points are assessed based

Question

Consider a game where a die is rolled three times and points are assessed based on the results.

(a) How many possible outcomes are there? (Assume that a roll of 2 3 5 is a dierent outcome from 3 2 5)

(b) What is the probability of rolling the same number three times?

(c) What is the probability of two of the rolls giving the same result and one roll being dierent?

(d) If you win $45 for rolling the same three numbers, lose $9 for only two rolls being the same, and get nothing for three dierent numbers, what is the expected value for this game?

Explanation / Answer

possible outcomes:

6*6*6=216

What is the probability of rolling the same number three times

ans (1/6 *1/6 *1/6) *6=1/36

What is the probability of two of the rolls giving the same result and one roll being dierent

ans( 1/6 *1/6 )*6*5/6 = 5/36

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