Suppose 5 men out of 100 and 25 women out of 1000 are good orators. An orator is chosen at random. Find the probability that a male person is selected. Assume that there are equal number of men and women.

Let us assume U₁, U₂ and A be the events as follows:

U₁ = choosing men

U₂ = choosing women

A = choosing orator

From the problems it is clear that men and women are equal in number. So, probability of choosing a men and women will be same.

⇒

⇒

From the problem:

⇒ P(A|U₁) = P(Choosing orator from men) =

⇒ P(A|U₂) = P(Choosing orator from women) =

Now we find

P(U₁|A) = P(The chosen orator is men)

Using Baye’s theorem:

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⇒

⇒

⇒

⇒

∴ The required probability is .