Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of these person being male? Assume that there are equal number of males and females.

Answer

N/a

Explanation

Let `E_(1)=` event of selecting a man,
`E_(2)=` event of selecting a woman,
and `E=` event of selecting a grey haired person.
Here `P(E_(1))=P(E_(2))=1/2`
`P(E//E_(1))=` probability of selecting a grey haired man `=5/100`
`P(E//E_(2))=` probability of selecting a grey haired woman
`=0.25/100`
Now required probability
`P(E_(1)//E)=(P(E_(1)).P(E//E_(1)))/(P(E_(1)).P(E//E_(1))+P(E_(2)).P(E//E_(2)))`
`=(1/2xx5/100)/(1/2xx5/100+1/2xx0.25/100)`
`=5/5.25=20/21`