Answer to Question #116629 in Statistics and Probability for Muzzamil

Question

The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that
(i) a married couple watches the show;
(ii) a wife watches the show, given that her husband does;
(iii) at least one member of a married couple will watch the show.

Answer 1

(i)P(man AND woman) = P(man|woman)*P(woman) = 0.7*0.5 = 0.35

(ii) P(woman|man) = P(man AND woman)/P(man) = 0.35/0.4 = 0.8750

(iii) P(man or woman) = P(man ) + P(woman) - P(man AND woman)= 0.4 + 0.5 - 0.35= 0.55