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.

a. Find the probability that both John and Jane watch the show.
b. Find the probability that Jane watches the show, given that John does.
c. Do John and Jane watch the show independently of each other? Justify your answer.:cool:

a. The probability of two events occurring is based on their respective probabilities. The probability of both is smaller than the probability of either, so choose your operation accordingly.
b. Conditional probability tells how often two events are likely to coincide... in this case, John watches the show at the same time as Jane 70% of the time that Jane watches it, so the overall time that they watch it together is 70% of 50%. The conditional probability you have to find is what percentage of John's 40% is spent with both of them watching.
c. With the conditional probabilities, you can see how the two relate overall.