Question

The probability that a man will live $10$ more years, is $\frac{1}{4}$ and the probability that his wife will live $10$ more years, is $\frac{1}{3}$. Then, what is the probability that neither will be alive in $10\, yr$?

• A. $\frac{1}{2}$
• B. $\frac{3}{7}$
• C. $\frac{2}{3}$
• D. $\frac{1}{4}$

Answer 1

Answer: (A)

Given,$ P(\bar{M})=\frac{1}{4}$
$\Rightarrow P(\bar{M})=1-\frac{1}{4}=\frac{3}{4}$
and $P(\bar{W})=\frac{1}{3}$
$\Rightarrow P(\bar{W})=1-\frac{1}{3}= \frac{2}{3}$
Here, both events are independent, so the required probability
$=P(\bar{W} \cap \bar{M})$
$=P(\bar{W}) \cdot P(\bar{M})$
$=\frac{3}{4} \times \frac{2}{3}$
$=\frac{1}{2}$