Answer to Question #140392 in Statistics and Probability for danish seth

Question

A new pub has opened in town and you’re considering it as a potential new spot for cheap
wings and beer. Before going, you chat with a group of 12 friends who have already been. You
obtain the following information:
Three of them complained about the quality of the beer.
Four of them complained about the quality of the wings.
Two of them complained about the quality of the beer and wings.
Three of them had no complaints.
Answer the following questions:
a. What is the probability you will enjoy the beer?
b. What is the probability you will enjoy the wings?
c. What is the probability you will dislike either the wings, or the beer, or both?
d. What is the probability you will enjoy both the beer and the wings?
e. Why have twelve of your friends already been here, but none have invited you

Answer 1

a. P(enjoy beer) = 1 – P(dislike beer), where 5 people dislike beer (3 dislike just beer + 2 dislike beer and wings)

hence P(enjoy beer) = $1 - \frac{5}{12}=\frac{7}{12}$

b. P(enjoy wings) = 1 – P(dislike wings), where 6 people dislike wings (4 dislike just wings + 2 dislike beer and wings)

hence P(enjoy beer) = $1 - \frac{6}{12}=\frac{6}{12}=\frac{1}{2}$

c. P(dislike either the wings, or the beer, or both) = P(dislike wings) + P(dislike beer) – P(dislike both) = $\frac{6}{12} + \frac{5}{12} - \frac{2}{12} = \frac{9}{12} = \frac{3}{4}$

or

P(dislike either the wings, or the beer, or both) = 1 – P(no complaints) = $1 - \frac{3}{12} = \frac{3}{4}$

d. P(enjoy both the beer and the wings) = 1 – P(dislike either the wings, or the beer, or both) = $1-\frac{3}{4}=\frac{1}{4}$

e. There is no sufficient information to answer this part of the question.