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

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#### 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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