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).

Question

Mathematics

Samson Greer

27 August, 22:24

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).

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Answers (1)

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

Step-by-step 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.