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? 1/18 1/9 1/4 1/2

Explanation:

Step1: Calculate total number of outcomes

When rolling two number - cubes (each with 6 sides), the total number of outcomes is \(6\times6 = 36\) according to the multiplication principle.

Step2: Find number of ways to get a sum of 11

The possible combinations to get a sum of 11 are \((5,6)\) and \((6,5)\), so there are 2 ways. The probability of winning (rolling 11) is \(P(\text{win})=\frac{2}{36}=\frac{1}{18}\).

Step3: Find number of ways to get an even sum

The sum of two numbers is even if both are even or both are odd. The number of ways to get both even: \(3\times3 = 9\) (since there are 3 even numbers on each cube: 2, 4, 6). The number of ways to get both odd: \(3\times3=9\). So the number of ways to get an even sum is \(9 + 9=18\). The probability of losing the next turn (rolling an even sum) is \(P(\text{lose next turn})=\frac{18}{36}=\frac{1}{2}\).

Answer:

What is the probability that he will win the game? A. \(1/18\)
What is the probability that he will lose his next turn? D. \(1/2\)