Question

4. Events X, Y, and Z are complementary, P(X) = 1/8. P(Y) = 1/2. What is the probability that Z will occur?

P(Z) is ____

Answer 1

3/8

Explanation:

You want the probability that Z will occur, given that events X, Y, and Z are complementary, P(X) = 1/8. P(Y) = 1/2.

Complementary events

Events are complementary when they are mutually exclusive and exhaustive. That is one, and only one, must occur. The total of probabilities of complementary events is 1.

P(Z) = 1 - P(X) - P(Y)

P(Z) = 1 - 1/8 - 4/8 = 3/8

The probability that Z will occur is 3/8.

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