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Suppose 5% of men and 0.25% of women have grey hair. A grey-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.

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Assume that there are 1000 men and 1000 women

MG as the men having grey hair, WG as the women having grey hair and G as the event of choosing an orator

P (MG) = 1000/2000 = 1/2

P (WG) = 1000/2000 = 1/2

We know that

P (G/MG) = 50/1000 = 1/20

P (G/WG) = 25/1000 = 1/40

Here we should determine

P (MG/G) – probability of a randomly selected grey haired person to be male

Substituting the values

On further calculation

= 1/40 × 80/3

= 2/3

Hence, the probability of a randomly selected grey haired person to be male is 2/3.

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