Question

# (a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that P(A1|B1).P(A2|B2)=P(A1|B2).P(A2|B1). (b) Let A and B1 be independent;...

(a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that

P(A1|B1).P(A2|B2)=P(A1|B2).P(A2|B1).

(b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1∪B2 are independent if and only if A and B1∩B2 are independent.

(c) Given P(A) = 0.42,P(B) = 0.25, and P(A∩B) = 0.17, find

(i)P(A∪B) ;

(ii)P(A∩Bc) ;

(iii)P(Ac∩Bc) ;

(iv)P(Ac|Bc).

Complete solution is given in attached images:

Thank You.

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