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, none of them will be alive

Solution

Let A ≡ event that man who is 45 will be alive till age 70.

B ≡ event that wife who is 40 will be alive till age 65.

It is given that,

P(A) = 5/12, P(B) = 3/8

∴ P(A') = 1 – P(A) = 1 - 5/12 = 7/12

∴ P(B') = 1 – P(B) = 1 - 3/8 = 5/8

A, B are independent

∴ A, B'; A', B; A', B' are also independent

P(none of them will be alive)

=P(A' ∩ B')

= P(A')·P(B')

= 7/12*5/8

= 35/96.

Concept: Independent Events
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