Question

If $P\left(A\right)=0.8,P\left(B\right)=0.5$ & $P\left(B/A\right)=0.4$ find (i) $P(A\cap B)$ (ii) $P\left(A/B\right)$ (iii) $P(A\cup B)$.

• A. $i)0.32,ii)0.64,iii)0.98$
• B. $i)0.62,ii)0.34,iii)0.88$
• C. $i)0.66,ii)0.32,iii)0.98$
• D. none

Answer 1

The correct option is A $i)0.32,ii)0.64,iii)0.98$

$P\left(\frac{B}{A}\right)=\frac{P(B\cap A)}{P\left(A\right)}0.4=\frac{P(B\cap A)}{0.8}$

$\therefore P(B\cap A)=0.32$, $⟹P(A\cap B)=0.32$

$thenP\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}=\left(\frac{0.32}{0.5}\right)=0.64$

$andP(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=0.8+0.5-0.32=0.98$