John and Jane are married. The probability that John watches a certain televisio

Question

John and Jane are married. The probability that John watches a certain television show is 0.7. The probability that Jane watches the show is 0.1. The probability that John watches the show, given that Jane does, is 0.8.

Find the probability that both John and Jane watch the show. (Round your answer to 2 decimal places.)

Find the probability that Jane watches the show, given that John does. (Round your answer to 3 decimal places.)

Do John and Jane watch the show independently of each other?

Find the probability that both John and Jane watch the show. (Round your answer to 2 decimal places.)

Explanation / Answer

John and Jane are married. The probability that John watches a certain television show is 0.7. The probability that Jane watches the show is 0.1. The probability that John watches the show, given that Jane does, is 0.8.

Let Jo shows the event that John watches a certain television show and Ja shows the event that Jane watches the show. So we have

P(Jo) = 0.7, P(Ja) = 0.1 and P(Jo |Ja) = 0.8

(a)

the probability that both John and Jane watch the show is

P(Jo and Ja) = P(Jo | Ja) P(Ja) = 0.8 * 0.1 = 0.08

(b)

the probability that Jane watches the show, given that John does

P(Ja | Jo) = P(Jo and Ja) / P(Jo) = 0.08 / 0.7 = 0.114

(c)

P(Jo) P(Ja) = 0.7 *0.1 = 0.07

P(Ja and Jo) and P(Jo)P(Ja) are not equal so John and Jane do notwatch the show independently of each other.

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