The probability that a 50-years-old man will be alive at 60 is `0.83` and the probability that a 45-years-old women will be alive at 55 is `0.87.` Then
`(a)`. Probability both the person are alive
`(b)`. Probability at least a person is alive

Options

A. the probability that both will be alive is `0.7221`
B. at least one of them will alive is `0.9779`
C. at least one of them will alive is `0.8230`
D. the probability that both will be alive is `0.6320`

Answer

A, B

Explanation

The probability that both will be alive for 10 years, hence, i.e., the probability that the man and his wife both will be alive 10 years hence is `0.83xx0.87=0.7221.` The probability that at least one of them will be alive is
1-p {That none of them remains alive 10 years hence}
`=1-(1-0.83)(1-0.87)=1-0.17xx0.13=0.9779`