Question

Suppose 5% men and 0.25% women has white hairs. A person with white hair is chosen at random. Find the probability that a male is selected. Assume that there are equal number of men and women.

Answer 1

Given that number of men and women are equal 

Let events 

E₁ = To be a man 

E₂ = To be a woman 

A = White hair

Probability to choose one man P(E₁) = 1/2

Probability to choose a women P(E₂) = 1/2

∴ Probability that a man has white hair

⇒ P(A/E₁) = 5% = 5/100 = 0.05

Probability that a woman has white hairs

⇒ P(A/E₂) = 0.25% = 25/100 = 0.25

Now, probability that male is selected

Hence, required probability = 20/21