Question

The probability that a married man watches a certain television show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that
a) a married couple watches the show
b) a wife watches the show given that her husband does;
c) at least 1 person of a married couple will watch the show.

Answer 1

a) a married couple watches the show

P(man|woman)=[P(man AND woman)]/[P(woman)]
Therefore (man AND woman) = P(man|woman)*P(woman) = 0.7*0.5 = 0.35.

b) a wife watches the show given that her husband does:

P(woman|man) = P(man AND woman)/P(man) = 0.35/0.4 = 0.8750

c) at least 1 person of a married couple will watch the show.



Need to figure out
P(both watch) = 0.35
P(man watches and woman does not) =P(man watches) - P(both watch)=0.40-0.35 = 0.05
P(woman watches and man does not) =P(woman watches) - P(both watch)= 0.50-0.35 = 0.15
P(at least 1 person of a couple will watch) =P(man watches and woman does not)+ P(woman watches and man does not)+P(both watch)=0.05+0.15+0.35 = 0.55

Therefore P(at least 1 person of a couple will watch)= 0.55.