Suppose 5 men out of 100 and 25 women out of 1000 are good orator. 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 event E1 be for choosing men, p(E1)=1/2
Let event E2 be for choosing women, p(E2)=1/2
Let A be the event for good orator.
P(A/E1)=5/100=1/20
p(A/E2)=25/1000=1/40
the probability of choosing a men
P(E1/A)= P(E1)P(A/E1)/  P(E1)P(A/E1)+ P(E2)P(A/E2)
by putting all the values
P(E1/A)=2/3