# 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:

The required probability is .

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