Question

The probability that a man A will be alive for 20 more years is $\frac{3}{5}$ and the probability that his wife will be alive for 20 more years is $\frac{2}{3}$, The probability that only one will be alive at the end of 20 years is

• A. $\frac{4}{15}$
• B. $\frac{2}{15}$
• C. $\frac{7}{15}$
• D. $\frac{8}{15}$

Answer 1

Answer: (C)

$\frac{7}{15}$

Answer 2

$P\left(A\right) =P\left(x \ge20\right) = \frac{3}{5}$ $P\left(B\right) =P\left(x \ge20\right) = \frac{2}{3}$ $P\left(A\cap\bar{B}\right)+ P\left(\bar{A} \cap B\right) = \frac{3}{5}. \frac{1}{3} + \frac{2}{5}. \frac{2}{3} = \frac{7}{15}$