If the probability that a man aged 60 will live to be 70 is 0.65 what is the probability that out of 10 men now 60 at least 8 will live to be 70 ?

Answer

`0.2615`

Explanation

`P(X ge 8) =P(X=8) +P(X=9) +P(X=10)`
`=[.^(10)C_(8).((13)/(20))^(8).((7)/(20))^(2)+.^(10)C_(9).((13)/(20))^(9).((7)/(20))+.^(10)C_(10).((13)/(20))^(10)]`
`=[.^(10)C_(2) .((13)/(20))^(8).(49)/(400)+.^(10)C_(1).((13)/(20))^(9).(7)/(20)+((13)/(20))^(10)]`
`:. P=((13)/(20))^(8).[(441)/(80) +(91)/(40)+(169)/(400)] =[((13)/(20))^(8)xx (821)/(100)]`
`rArr " log =P [8 (log 13 -log 20) + log 821 - log 100"]`
`=[-1.4968 +2.9143 -2] =-0.5825`
`=1.4175`
`rArr P=" antilog "(bar(1).4175)`