The probability that a man lives after 10 years is 1/4. The probability that his wife is alive after 10 years is 1/ 3. Find the probability that neither of them is alive after 10 years. 

Probability that a man live more than 10 years = 1/4.
Probability that man not live more than 10 years = 1- 1/4 = 3/4.
Probability his wife live more than 10 years = 1/3.
Probability his wife not live 10 years = 1- 1/3 = 2/3.

Hence, the required probability, 

$\begin{array}{l}P(\overline{M}\cap \overline{W})=P\left(\overline{M}\right)\cdot P\left(\overline{W}\right)\\ =\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}\end{array}$