Question

If $P(A)=0.8,P(B)=0.5$ and $P(B/A)=0.4$, then match the terms of column I with the terms of column II and choose the correct option from the codes given below.

Column I		Column II
A	$P(A\cap B)$	1	$0.64$
B	$P(A/B)$	2	$0.98$
C	$P(A\cup B)$	3	$0.32$

• A. A- 1 ,B- 2 ,C- 3
• B. A- 3 ,B-1 ,C- 2
• C. A-2,B- 3 ,C- 1
• D. A-1,B- 2 ,C- 3

Answer 1

Answer: (B)

A. Given, $P(A)=0.8,P(B)=0.5,P\left(\frac{B}{A}\right)=0.4$
$\Rightarrow \frac{P(A\cap B)}{P(A)}=0.4\left[\because P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P(A)}\right]$
$\Rightarrow \frac{P(A\cap B)}{0.8}=0.4$
$\Rightarrow P(A\cap B)=0.8\times 0.4$
$=0.32$
B. $P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P(B)}=\frac{0.32}{0.5}=\frac{32}{50}=0.64$
C. From the relation, $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$=0.8+0.5-0.32$
$=1.3-0.32=0.98$