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 \quad\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, $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$=0.8+0.5-0.32$
$=1.3-0.32=0.98$