Question

Analyzing a Situation
Jeff can win the game if he rolls 11 on the two number cubes. If he rolls an even sum, however, he will lose his next turn.

What is the probability that he will win the game?
What is the probability that he will lose his next turn?

Answer 1

Two fair six-sided dice give 36 equally likely outcomes.

- Ways to roll an 11: (5,6) and (6,5) → 2/36 = 1/18.
- Ways to get an even sum: sums 2,4,6,8,10,12 occur 18 ways → 18/36 = 1/2.

So P(win) = 1/18, and P(lose next turn) = 1/2.