Consider the independent events $A$ and $B$. Given that $P(B) = 2P(A)$, and \(P(A ∪ B) =

Question

Consider the independent events $A$ and $B$. Given that $P(B) = 2P(A)$, and $P(A ∪ B) = 0.52$, find $P(B)$.[7]

Accepted Answer

Let $P(A)=a$, so $P(B)=2a$. Independence gives $0.52=a+2a-2a^2$. Thus $2a^2-3a+0.52=0$, with admissible root $a=0.2$. Hence $P(B)=0.4$.

Solve event probabilities using independence and the union rule.