Let the events M, F and G be defined as follows:
M: A male is selected
F: A female is selected
G: A person has grey hair
It is given that the number of males = the number of females
∴ P (M) = P (F) =

1

2

Now, P (G/M) = Probability of selecting a grey haired person given that the person is a:
Male = 5% =

5

100

Similarly, P (G/F) = 0.25% =

0.25

100

A grey haired person is selected at random, the probability that this person is a male = P(M|G)
= [Using Baye’s Theorem]
=

1 2 × 5 100

1 2 × 5 100 + 1 2 × 0.25 100

=

5 100

5 100 + 0.25 100

=

5

5.25

=

20

21