Question

Suppose that 5 men out of 100 and 25 women out of 1000 are good orators. Assuming that there are equal number of men and women, find the probability of choosing a good orator.

Answer 1

P(Men good orator) = `5/100`

P(Women good orator) = `25/1000`

P(of choosing good orator) = ?

Let E₁ and E₂ denote the events that the person is a good orator.

E₁ = Man orator, P(E₁) = `1/2`

E₂ = Woman orator, P(E₂) = `1/2`

A = Selecting good orator

P(A / E₁) = `5/100`, P(A / E₂) = `25/1000`

Required Probability

P(A) = P(E₁) × P(A / E₁) + P(E₂) × P(A / E₂)

= `1/2 xx 5/100 + 1/2 xx 25/1000`

= `3/80`