Question

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

• A. $\frac{3}{5}$
• B. $\frac{1}{2}$
• C. $\frac{4}{15}$
• D. $\frac{13}{15}$

Answer 1

The correct option is D $\frac{13}{15}$

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 $P\left(B\right)=\frac{2}{3}$

Hence, the probability that atleast one will be alive is $P\left(A\right)+P\left(B\right)-\left(P\right(A)\times P(B\left)\right)=\frac{3}{5}+\frac{2}{3}-(\frac{3}{5}\times \frac{2}{3})=\frac{9+10-6}{15}=\frac{13}{15}$