Ethan, Matt and Adam are three friends who participate in a monthly math competi

Question

Ethan, Matt and Adam are three friends who participate in a monthly math competition. Each month, the probability that Ethan will score higher than Matt is 50%; the probability that Ethan will score higher than Adam is 90%; the probability that Ethan will score higher than neither Mat nor Adam is 5%.

1. Find the probability that Ethan scores higher than at least one of his two friends. 2. Find the probability that Ethan scores higher than Adam but not Matt. 3. Find the probability that Ethan scores higher than both Matt and Adam.

Explanation / Answer

1) P(Ethan score higher than at least one of these two friends) = 0.5 * 0.1 + 0.9 * 0.5 + 0.5 * 0.9 = 0.95

2) P(Ethan score higher than Adam but not Matt) = 0.9 * 0.5 = 0.45

3) P(Ethan score higher than both Matt and Adam) = 0.5 * 0.9 = 0.45

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