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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{1}{2}\)
“None of them” means the man does not live 10 more years and his wife does not. The two events are independent, so their probabilities are multiplied; each comes from P(not E) \(=1-\) P(E).
The man does not live 10 more years: \(\displaystyle 1-\frac{1}{4}=\frac{3}{4}\)
The wife does not live 10 more years: \(\displaystyle 1-\frac{1}{3}=\frac{2}{3}\)
Neither lives 10 more years: \(\displaystyle \frac{3}{4}\times\frac{2}{3}=\frac{1}{2}\)