Question

Let A and B be events such that P(A) = 0.6, P(A È B) = 0.8 and P(A | B) = 0.6.

Find P(B).

Answer 1

$P(A\ and\ B)=P(A)P(B|A)=0.6\cdot 0.8=0.48$

$P(B)=\frac{P(A\ and\ B)}{P(A|B)}=\frac{0.48}{0.6}=0.8$