If A and B are two independent events such that P (A ∪ B) = 0.60 and P(A)= 0.2, find P(B).
Given that A and B are independent events,
We know that,
P (A ∪ B)=P(A)+P(B)–P(A∩B)
Therefore,
P (A ∪ B)=P(A)+P(B)–P(A∩B)
=P(A)+P(B)–[P(A)*P(B)]
0.6=0.2+P(B)–0.2P(B)
0.6–0.2=P(B)[1–0.2]
0.4=P(B)*0.8