john and jane are married. the probability that john watches a certain television show is .4. the probability that Jane watches the show is .5. the probability that john watches the show given that jane does is .7. find the probability that both john and jane watches the show given that jane does, find the probability the jane watches the show that john does. do john and jane watch the show independently of each other justify your answer Solution P(John)= .4, P(Jane)= .5, P(John|Jane)=.7 a. P(John and Jane)=? P(John|Jane)=P(John and Jane)/P(Jane) P(John and Jane)= P(John|Jane)*P(Jane)= .7 * .5= .35 b.P(Jane|John)=? P(Jane|John)= [P(John|Jane)*P(Jane)]/P(John)= (.7 * .5)/ .4 = .875 c.No, they do not watch shows independently. If they watched shows independently then P(John|Jane)= P(John) which does not hold in this example..