Mathematics

Mathematics

Problem

For events AA and BB with probabilities P(A)=pP(A)=p, P(B)=qP(B)=q (0<p,q<1)(0<p,q<1), suppose P(A∪B)=p+q−2pq.P(A\cup B)=p+q-2pq. Which of the following describes their independence? a) They are independent only when p=qp=q. b) They are never independent for 0<p,q<10<p,q<1. c) They are independent for all pp and qq. d) They are independent only when p=0p=0 \text{ or } q=0$.

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