Question

For the married couple living in Jammu, the probability that a husband will vote in an election is $0.5$ and the probability that his wife will vote is $0.4$ . The probability that the husband votes, given that his wife also votes is $0.7$ . Then, the probability that husband and wife both will vote is

• A. $0.28$
• B. $0.20$
• C. $0.35$
• D. $0.15$

Answer 1

Answer: (A)

$0.28$

Answer 2

Given, $P\left( \frac{H}{F} \right)=0.7,\,\,P(H)=0.5$
and $P\,\,(W)=0.4$
$\therefore$ $P\left( \frac{H}{W} \right)=\frac{P(H\cap W)}{P(W)}$
$\therefore$ $0.7=\frac{P(H\cap W)}{0.4}$
$\Rightarrow$ $P(H\cap W)=0.28$