Question

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

Answer 1

It is given that men with grey hair are 5% and women with grey hair are 0.25%.

Let A be the event that men have grey hair and B be the event that women have grey hair.

The total percentage of people that have grey hair is,

( A+B )%=( 5+0.25 )% =5.25%

The probability that the selected haired person is a male is,

P= A A+B = 5 5.25 = 20 21

Therefore, the required probability is 20 21 .