Question

The probability that a man will be alive in 40 years is 3/5, and the probability that his wife will also survive 40 years is 2/3. Find the probability that only the man will survive.

• A. $\frac{3}{5}$
• B. $\frac{1}{5}$
• C. $\frac{1}{3}$
• D. $\frac{10}{15}$

Answer 1

Answer: (B)

$\frac{1}{5}$

Given the probability that a man will be alive in 40 years is $P\left(A\right)=\frac{3}{5}$

and, the probability that his wife will also survive 40 years is $P\left(B\right)=\frac{2}{3}$

Considering these two probabilities are independent. Hence, the probability that only the man will survive is $P\left(A\right)\times P\left(\overline{B}\right)=\frac{3}{5}\times (1-\frac{2}{3})=\frac{3}{5}\times \frac{1}{3}=\frac{1}{5}$