If P(A lives 15 years) = 7/8 and P(B lives 15 years) = 9/10, assuming independence, what is the probability that both A and B are alive after 15 years?

Introduction / Context:For independent events, the probability that both occur equals the product of their individual probabilities. Survival-type questions often include this assumption unless stated otherwise.

Given Data / Assumptions:

• P(A survives 15 years) = 7/8.
• P(B survives 15 years) = 9/10.
• Independence of the two survival events (as typical in basic probability exercises).

Concept / Approach:P(A ∩ B) = P(A) * P(B) for independent A and B.

Step-by-Step Solution:P = (7/8) * (9/10) = 63/80.

Verification / Alternative check:63/80 = 0.7875 lies between individual probabilities (0.875 and 0.9), as expected for a conjunction.

Why Other Options Are Wrong:1/20 and 1/5 are far too small; “None of these” is incorrect since 63/80 is present.

Common Pitfalls:Adding probabilities instead of multiplying for independent “both happen” scenarios.

Final Answer:63/80