Find the probability of the following

Question

The probability that a married man watches a certain television show is 1/2 and the probability that a married woman watches the show is 2/5. The probability that a man watches the show, given that his wife does, is 4/5. Find the probability that a married couple do not watch the show.

Answer 1

Probability both man and woman of a married couple do Not what the show is:

68% = 17/25

P(m) = 1/2

P(w) = 2/5

P(m/w) = 4/5

P(m^w)P(w) = P(m/w)

P(m^w) = P(m/w)P(w) = (4/5)(2/5) = 8/25

=P(w^m) = P(w/m)P(m) = (16/25)(1/2) = 8/25

Probability a married couple does not watch the show = 1-8/25 = 25/25-8/25 = (25-8)/25 = 17/25= 68/100

=.068

= 68%

Use Bayes' Theorem to find P(w/m)=16/25

P(m)P(w/m) = P(w)P(w/m)

P(m)P(w/m) =(1/2)P(w/m)

= P(w)P(m/w) = (2/5)(4/5) = 8/25

P(w/m) = (8/25)/(1/2) = 16/25

P(w/m) = 16/25