In a certain city, the ratio of men to women is 5:4 . It is found that 80 % of men and 90 % of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....

Step-by-step solution

Let M and W be the events that the selected person is a man and a woman respectively. P(M) = 5 9 and P(W) = 4 9 Let I be the event that the selected person is illiterate. Given that 80 % of men and 90 % of women are literate, the probabilities of them being illiterate are: P(I|M) = 1 - 0.8 = 0.2 = 1 5 P(I|W) = 1 - 0.9 = 0.1 = 1 10 By Bayes' theorem, the probability that the person is a man given that they are illiterate is: P(M|I) = P(M)P(I|M) P(M)P(I|M) + P(W)P(I|W) P(M|I) = 5 9 1 5 5 9 1 5 + 4 9 1 10 P(M|I) = 1 9