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Question
The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that the couple will be alive 20 years hence.
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Solution
Let A be the event that husband would be alive after 20 years.
Odds against A are 8: 5
∴ The probability of occurrence of event A is given by
P(A) = `5/(8 + 5) = 5/13`
∴ P(A') = 1 – P(A) = `1 - 5/13 = 8/13`
Let B be the event that wife would be alive after 20 years.
Odds against B are 4: 3
∴ The probability of occurrence of event B is given by
P(B) = `3/(4 + 3) = 3/7`
∴ P(B') = 1 – P(B) = `1 - 3/7 = 4/7`
Since A and B are independent events
∴ A' and B' are also independent events
Let X be the event that both will be alive after 20 years.
∴ P(X) = (A ∩ B)
∴ P(X) = P(A).P(B) = `5/13 xx 3/7 = 15/91`
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