odds are 8:5 against a man who is 55 years old, living till he is 75 and 4:3 against his wife who is now 48, leaving till she is 68. find the probability that one couple will be alive live 20 years hence.
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The probability that the man will be alive in 20 years time = 5/13
The probability that the man will be dead in 20 years time = 8/13
The probability that the wife will be alive in 20 years time = 3/7
The probability that the woman will be dead in 20 years time = 4/7
the probability that either of them will be alive in 20 years time
= the probability that the man is a live and the woman is dead OR the man is dead and the woman is alive
= 5/13 x 4/7 + 8/13 x 3/7
= 20/91 + 24/91
= 44/91
See the Probability tree below:
The probability that the man will be dead in 20 years time = 8/13
The probability that the wife will be alive in 20 years time = 3/7
The probability that the woman will be dead in 20 years time = 4/7
the probability that either of them will be alive in 20 years time
= the probability that the man is a live and the woman is dead OR the man is dead and the woman is alive
= 5/13 x 4/7 + 8/13 x 3/7
= 20/91 + 24/91
= 44/91
See the Probability tree below:
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