Question

Suppose that two fair dice are tossed. What is the probability that the sum equals 10 given that it exceeds 8?

a) 1/12
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b) 1/9

c) 1/6
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d) 1/4

Answer 1

The probability that the sum of two fair dice equals 10 given that it exceeds 8 is 1/3.

Step-by-step explanation:

To find the probability that the sum of two fair dice equals 10 given that it exceeds 8, we first need to determine the number of favorable outcomes and the total number of possible outcomes.

When two dice are rolled, the ways to obtain a sum of 10 are (4,6), (5,5), and (6,4), which is a total of 3 favorable outcomes. When the sum exceeds 8, the favorable outcomes are (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), and (6,6), which is a total of 10 outcomes.

The probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes:

P(sum equals 10 | exceeds 8) = 3/10 = 1/3