The events A and B are independent such that $P(B)$ = 3$P(A)$ and $P(A∪B)$ = 0.68. Find \(P(B)

Question

The events A and B are independent such that $P(B)$ = 3$P(A)$ and $P(A∪B)$ = 0.68. Find $P(B)$

Accepted Answer

Let $P(A)=a$, so $P(B)=3a$. Independence gives $0.68=4a-3a^2$. The admissible root is $a=0.2$, so $P(B)=0.6$.

Solve event probabilities using independence and the union rule.