Question

In a population, 20% of the people are senior citizens. Among the senior citizens, 65% are female, but among those who are not senior citizens, 50% are female. One person is picked at random. Find ?(person is a senior citizen | person is female).

Answer 1

P(senior citizens) = 0.2

P(female | senior citizen) = 0.65

P(female | not senior citizen) = 0.5

P(female) = P(female | senior citizen) * P(senior citizen) + P(female | not senior citizen) * P(not senior citizen)

                 = 0.65 * 0.2 + 0.5 * (1 - 0.2)

                 = 0.53

P(senior citizen | female) = P(female | senior citizen) * P(senior citizen) / P(female)

                                         = 0.65 * 0.2 / 0.53

                                         = 0.245