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Distinguish dependence from a nonempty overlap

Two events A and B satisfy P(A)=1/4P(A)=1/4, P(A∣B)=1/2P(A\mid B)=1/2 and P(B∣A)=2/3P(B\mid A)=2/3.

(i) Determine whether A and B are independent, justifying your answer.

(ii) Determine whether A and B are mutually exclusive, justifying your answer.

(iii) Find P(B).

CJC · Lecture · Example 3

Name the events, identify the sample space, and state which outcomes or conditions are being counted.

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