(MASTERY Problem) Chapter 3 Review Practice Problems, Problem 18: Enrollment dat

Question

(MASTERY Problem) Chapter 3 Review Practice Problems, Problem 18: Enrollment data at a certain college shows that 30% of the men and 10% of the women are studying statistics and that the men form 45% of the student body. If a student is selected at random and is found to be studying statistics (S), determine the probability that the student is a woman (W). First, what are the following conditional probabilities (read them carefully) P(SIW')- Next, what are the following joint probabilities: Being a woman and studying statistics, P(W n S) = Not being a woman and studying statistics, P(W' n Finally, what is the probability that a student found to be studying statistics happens to be a woman? P(W | S) =

Explanation / Answer

P(S | W') = 0.3

P(S | W) = 0.1

P(W) = 1 - 0.45 = 0.55

P(W S) = P(S | W) * P(W) = 0.1 * 0.55 = 0.055

P(W' S) = P(S | W') * P(W') = 0.3 * 0.45 = 0.135

P(S) = P(W S) + P(W' S) = 0.055 + 0.135 = 0.19

P(W | S) = P(W S) / P(S) = 0.055 / 0.19 = 0.2895

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