Independent survival over 10 years: P(man lives 10y) = 1/4, P(wife lives 10y) = 1/3. What is the probability that after 10 years neither is alive?

Introduction / Context:We are given survival probabilities over a fixed horizon for two people and asked for the probability that neither survives. Assume independence unless stated otherwise.

Given Data / Assumptions:P(M survives) = 1/4 ⇒ P(M dies) = 3/4; P(W survives) = 1/3 ⇒ P(W dies) = 2/3; independence assumed.

Concept / Approach:P(neither alive) = P(M dies) * P(W dies).

Step-by-Step Solution:

Verification / Alternative check:Complement perspective: 1 − P(at least one survives) = 1 − [1 − P(neither)] ⇒ consistent when computing directly.

Why Other Options Are Wrong:5/12 and 7/12 arise from mixing survival vs failure; 11/12 is impossible here.

Common Pitfalls:Confusing given survival with failure probabilities; overlooking independence.

Final Answer:1/2