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, the probability that none of them will be alive after $10$yrs is.

• A. $\frac{5}{12}$
• B. $\frac{1}{2}$
• C. $\frac{7}{12}$
• D. $\frac{11}{12}$

Answer 1

The correct option is B $\frac{1}{2}$

The probability that a man will not alive after $10$yrs $=1-\frac{1}{4}=\frac{3}{4}$
The probability that his wife will not alive after $10$yrs $=1-\frac{1}{3}=\frac{2}{3}$
Now, the probability that none of them will be alive after $10$yrs $=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}$