Question

The probability that a man will be alive in $40$ years is $\frac{3}{5}$, and the probability that his wife will also survive $40$ years is $\frac{2}{3}$. Find the probability that both will be alive

• A. $\frac{2}{5}$
• B. $\frac{4}{5}$
• C. $\frac{2}{15}$
• D. $\frac{6}{15}$

Answer 1

The correct option is A $\frac{2}{5}$

Given the probability that a man will be alive in $40$ years is $\frac{3}{5}$

and, the probability that his wife will also survive $40$ years is $\frac{2}{3}$

Considering these two probabilities are independent. Hence, the probability that both will be alive is $\frac{3}{5}\times \frac{2}{3}=\frac{2}{5}$