Question

Let $A$ and $B$ be independent events with $P\left(A\right)=0.2,P\left(B\right)=0.5$. Then find:
(i) $P\left(A|B\right)$
(ii) $P\left(B|A\right)$
(iii) $P(A\cap B)$
(iv) $P(A\cup B)$

Answer 1

If $A$ and $B$ are independent events then $P(A\cap B)=P\left(A\right)P\left(B\right)=0.2\times 0.5=0.1$

Therefore,

(i) $P\left(A|B\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{P\left(A\right)P\left(B\right)}{P\left(B\right)}=P\left(A\right)=0.2$
(ii) $P\left(B|A\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{P\left(A\right)P\left(B\right)}{P\left(A\right)}=P\left(B\right)=0.5$
(iii) $P(A\cap B)=0.1$
(iv) $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=0.2+0.5-0.1=0.6$