# The probability that a man who is 45 years old will be alive till he becomes 70 is 512. The probability that his wife who is 40 years old will be alive till she becomes 65 is 38. What is the probabil - Mathematics and Statistics

Sum

The probability that a man who is 45 years old will be alive till he becomes 70 is 5/12. The probability that his wife who is 40 years old will be alive till she becomes 65 is 3/8. What is the probability that, 25 years hence, exactly one of them will be alive

#### Solution

Let event A : The man will be alive till 70.

∴ P(A) = 5/12

Let event B : The wife will be alive till 65.

∴ P(B) = 3/8

∴ P(A') = 1 – P(A) = 1 - 5/12 = 7/12

P(B') = 1 – P(B) = 1 - 3/8 = 5/8

Since A and B are independent events,

A' and B' are also independent events.

Let event D : Exactly one of them will be alive.

∴ P(D) = P(A' ∩ B) + P(A ∩ B')

= P(A')·P(B) + P(A)·P(B')

= (7/12 xx 3/8) + (5/12 xx 5/8)

= 21/96 + 25/96

= 46/96

= 23/48.

Concept: Independent Events
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