Question

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.

Answer 1

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.

⇒ P(U₁) = \(\cfrac12\)

 ⇒ P(U₂) = \(\cfrac12\)

From the problem:

⇒ P(A|U₁) = P(Choosing orator from men) = \(\cfrac5{100}\)

⇒ P(A|U₂) = P(Choosing orator from men) = \(\cfrac{25}{1000}\)

Now we find

P(U₁|A) = P(The chosen orator is men)

Using Baye’s theorem:

∴ The required probability is \(\cfrac23.\)