The probability that a wife W watches a certain television show is 0.31, that her husband H watches it is 0.21, and that both watch the show is 0.05. What is the probability, to two decimal places, that either the husband or the wife watches this show?
A)Pr(H∪W) = 0.21
B)Pr(H∪W) = 0.05
C)Pr(H∪W) = 0.57
D)Pr(H∪W) = 0.47
E)Pr(H∪W) = 0.52

Question

The probability that a wife W watches a certain television show is 0.31, that her husband H watches it is 0.21, and that both watch the show is 0.05. What is the probability, to two decimal places, that either the husband or the wife watches this show? ​
A)Pr(H∪W) = 0.21
B)Pr(H∪W) = 0.05
C)Pr(H∪W) = 0.57
D)Pr(H∪W) = 0.47
E)Pr(H∪W) = 0.52

Quizplus · Accepted Answer

We need to find the probability of either the husband or the wife watching the show. This can be represented as the union of events H and W (i.e. H or W or both). We can use the formula:
Pr(H∪W) = Pr(H) + Pr(W) - Pr(H∩W)
where Pr(H∩W) represents the probability of both the husband and the wife watching the show. 
Substituting the given values:
Pr(H∪W) = 0.21 + 0.31 - 0.05 = 0.47
Therefore, the probability that either the husband or the wife watches the show is 0.47 or 47%. Therefore, the answer is D.

The Probability That a Wife W Watches a Certain Television