please solve asap. thanks Q2. (Text 2.81) It is determined that married men watc

Question

please solve asap.
thanks

Q2. (Text 2.81) It is determined that married men watch a certain TV show with probability 0.4, and that married women watch the show with probability 0.75. In addition, it is determined that the probability that a man watches the show, given that his wife watches the show, is 0.7. Find the probability that: a) A randomly selected married couple both watch the show b) A woman watches the show, given that her husband watches the show c) At least one member of a married couple watch the show.

Explanation / Answer

Question 2:

Here we are given that the probability that man watches the show is 0.4. Therefore P(M) = 0.4

Probability that the woman watches the show is 0.75 that is P(W) = 0.75

Also Given that wife watches the shows, probability that man watches the show is 0.7. Therefore we have here:

P( M | W) = 0.7

a) Using Bayes theorem we get:

P( M | W) = P( M and W) / P(W)

Therefore: P( M and W) = P( M | W) P(W) = 0.7*0.75 = 0.525

Therefore 0.525 is the required probability here. ( but this is not possible because the total probability that a man watches the show is only 0.4 ) Therefore there is some error in the given probabilities.

b) Probability that a woman watches the show given that her husband watches the show:

P( W | M)

Again using Bayes theorem we get:

P( W|M) = P(W and M)/ P(M) = 0.525 / 0.4 > 1 that is not possible ( therefore there was some error in the given original probabilities )

c) At least one member of the married couple watches the show:

P( M or W) by addition law can be computed as:

P(M or W)= P(M) + P(W) - P(M and W)

P(M or W) = 0.4 + 0.75 - 0.525 = 0.625

Therefore 0.625 is the required probability here.

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