Question

Given P(A) = 0.9 and P(B) = 0.6, Find the following:

Find the maximum and minimum for P(A U B)

Find the maximum and minimum for P(AB)

Answer 1

for A u B

maximum for P(A u B) =min(1, P(A)+P(B))=min(1,0.9+0.6)= 1

minimum of P(A u B) =max(A,B)=max(0.9,0.6) =0.9

for AB

maximum for AB =min(A,B) =min(0.9,0.6)=0.6

minimum of AB =max((P(A)+P(B))-1,0)=max(0.9+0.6-1,0) =max(0.5,0)=0.5