Answer to Question #280216 in Statistics and Probability for tk98

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

Solution;

Given;

$P_M=0.4$

$P_W=0.5$

$P_{M|W}=0.7$

(a)

$P_{MW}=P_{M|W}×P_W=0.7×0.5=0.35$

$(b)$

$P_{W|M}=\frac{P_{MW}}{P_M}=\frac{0.35}{0.4}=0.8750$

$(c)$

$P_{MorW}=P_M+P_W-P_{MW}=0.4+0.5-0.35=0.55$