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Worked solution

Recover an intersection from a conditional probability

Events A and B satisfy P(B)=2/3P(B)=2/3 and P(A∣B)=3/5P(A\mid B)=3/5. Find P(A∩B)P(A\cap B).

CJC · Lecture · Self-Practice 2

Multiply by the conditioning-event probability

Use P(A∩B)=P(A∣B)P(B)=(3/5)(2/3)=2/5=0.4P(A\cap B)=P(A\mid B)P(B)=(3/5)(2/3)=2/5=0.4. The printed answer 0.4 is retained; this derivation supplements the answer-only source.

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Common mistakes

This is the conditional multiplication rule; independence is not assumed or needed.

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