Question

The odds against for a husband, who is 45 year-old living till 70 is 7:5. and the odds against for his wife who is 36 year-old living till 61 is 5:3. The probability that at least one of them will be alive 25 years hence,is*

Answer 1

The probability that the couple will be alive is 61 / 96.

Explanation:

P (A) / P (A) = odd i favour of A

Odds against P(A) / P(A)

H : Husband lives till 70

P(H) = P(H) / P(H) = 7 / 5

P(Ho) = 5 / 12 P(H) = 7 / 12

Now W : Wife lives till 61

P(W) / P(W) = 5 / 3

P(W) = 3 /8

P(W) = 5 / 8

P(H ⋂ W)  = P (H)/( 5 /12) : P(W) / (3/8)

P(H ⋂ W)  = 15

Now

P(A) + P(B) - 2 P(A ⋂ B)     [ P(H ⋂ W)  = Pi ]

P(H) + P(W)  - 2 P (H ⋂ W)

5 / 12 + 3 /8 - 2 ( 5 /12 ) (3 /8)

P (H ⋂ W) = P(H) . P(W)

P (H ⋂ W) = 7 /12 . 5 / 8 = 35 / 96

P (H ⋃ W)  = P(H) + P(W) - P (H ⋂ W)

P (H ⋃ W)  =  5 / 12 + 3 /8 - 5 /12 . 3 /8

P (H ⋃ W)  = 76 / 96 - 15 / 96 = 61 / 96