In a class, 60% of students study French. Of those who study French, 30% also study German. Of those who do not study French, 50% study German. What is the probability that a randomly chosen student studies both French and German?

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Question

In a class, 60% of students study French. Of those who study French, 30% also study German. Of those who do not study French, 50% study German. What is the probability that a randomly chosen student studies both French and German?

Accepted Answer

A) 0.18 — P(French and German) = P(French) × P(German | French) = 0.6 × 0.3 = 0.18. This is found by multiplying along the relevant branches of the tree diagram. Option B incorrectly uses P(German | French) alone.

Answer

A) 0.18

Answer

B) 0.30

Answer

D) 0.20

Answer

C) 0.50

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