Answer to Question #152610 in Statistics and Probability for Yosef

Question

Suppose that a customer buys bread 1/2 of the time, buys butter 1/4 of the time, and both bread and butter 1/8 of the time.

1. What is the probability that he buys either bread or butter or both? 2. What is the probability that he buys neither bread nor butter?

Answer 1

Let event A = buying bread

B= buying butter

given probabilities

P(A) = 1/2 , P(B) = 1/4 , P(A ⋂ B) = 1/8

1. We need P( A U B) .

P( A U B) = P(A) + P(B) - P(A ⋂ B) = 1/2 + 1/4 - 1/8 = 5/8

2.We need P( (A U B)^C)

P( (A U B)^C) = 1 - P( A U B) = 1 - 5/8 = 3/8