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John & Jane are married. T hje probablity that John wathces a cert.pdf

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John & Jane are married. T hje probablity that John wathces a certain television show is .4. the probability jane watches the show is .5. The probability that John watches the show, given that Jane does is .7. a) Find the probability that both John and Jane watch the show b) Find the probability that Jane watches the show, given John does c) Do John & Jane watch the show independently of each other? Justify 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..

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John & Jane are married. T hje probablity that John wathces a certain television show is .4. the probability jane watches the show is .5. The probability that John watches the show, given that Jane does is .7. a) Find the probability that both John and Jane watch the show b) Find the probability that Jane watches the show, given John does c) Do John & Jane watch the show independently of each other? Justify 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.

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  • 1. John & Jane are married. T hje probablity that John wathces a certain television show is .4. the probability jane watches the show is .5. The probability that John watches the show, given that Jane does is .7. a) Find the probability that both John and Jane watch the show b) Find the probability that Jane watches the show, given John does c) Do John & Jane watch the show independently of each other? Justify 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.