Question

If $A$ and $B$ are two events, such that $P\left(A\right)=0.3,P\left(B\right)=0.6$ and $P\left(B/A\right)=0.5$, then $P(A\cup B)=$

Answer 1

Conditional Probability, $P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}$

$P(A\cap B)=P\left(\frac{B}{A}\right)\times P\left(A\right)$

$=0.5\times 0.3$

$=0.15$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=0.3+0.6-0.15$

$=0.75$