Question

Five hundred employees were selected from various companies and asked whether they had retirement benefits at work. Their replies are in the table. Are the events W = "is a woman" and B = "has benefits" independent? Why or why not? A) Yes; because P(W & B) = P(W) + P(B). B) No; because P(W & B) ≠ P(W) + P(B). C) Yes; because P(W & B) = P(W) · P(B). D) No; because P(W & B) ≠ P(W) · P(B).

Answer 1

C) Yes; because P(W & B) = P(W) · P(B).

Explanation:

Yes; because P(W & B) = P(W) · P(B). P(W) = 200/500 = 0.4, P(B) = 375/500 = 0.75, and P(W & B) = 150/500 = 0.3. Notice that (0.4)(0.75) = 0.3.