The probability that a man will live for 10 more years is $\frac{1}{4}$ and the probability that his wife will live for 10 more years is $\frac{1}{3}$. The probability that none of them will live for 10 more years is

$\frac{1}{2}$

The probability that a man will live for 10 more years = $\frac{1}{4}$

The probability that a man will not live for 10 more years = 1 - $\frac{1}{4}$= \(\frac{3}{4}\)

The probability that his wife will live for 10 more years = $\frac{1}{3}$

The probability that his wife will not live for 10 more years = 1 - $\frac{1}{3}$ = \(\frac{2}{3}\)

So, probability that none of them will live for 10 more years = \(\frac{3}{4}\) × \(\frac{2}{3}\) = \(\frac{1}{2}\)