Question

Find P(AUB) when 2P(A)=P(B)=$\frac{5}{13}$and P(A|B)=$\frac{2}{5}$.

Answer 1

$P\left(A|B\right)=\frac{P(A\cap B)}{P\left(B\right)}\frac{2}{5}=\frac{P(A\cap B)}{5/13}P(A\cap B)=2/13P\left(AUB\right)=P\left(A\right)+P\left(B\right)-P(A\cap B)=3P\left(A\right)-\frac{2}{13}=\frac{15}{26}-\frac{2}{13}=11/26$