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Question

The probability that a man will live 10 more years, is 14 and the probability that his wife will live 10 more years, is 13. Then, what is the probability that neither will be alive in 10 years?

A
12
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B
37
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C
23
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D
14
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Solution

The correct option is A 12
let M be the event that the man will live 10 years more
let W be the event that the wife will live 10 years more

Given, P( M)=14P(¯M)=114=34
and P( W)=13P(¯W)=113=23
Here, both events are independent, so the required probability
=P(¯W¯M)
=P(¯W)P(¯M)
=34×23
=12

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