Answer to Question #126785 in Statistics and Probability for jaya

Question

b) A restaurant manager classifies customers as regular, occasional, or new, and finds that of all
customers 50%, 40%, and 10%, respectively, fall into these categories. The manager found that
wine was ordered by 70% of the regular customers, by 50% of the occasional customers, and by
30% of the new customers.
I. What is the probability that a randomly chosen customer orders wine?
II. If wine is ordered, what is the probability that the person ordering is a regular
customer?
III. If wine is ordered, what is the probability that the person ordering is an occasional
customer?

Answer 1

For the given information , we draw the following tree diagram.

I)

probability that a randomly chosen customer orders wine=

(0.5*0.7)+(0.4*0.5)+(0.1*0.3)

=0.58

II)If wine is ordered, what is the probability that the person ordering is a regular customer:

Using conditional probability formula, P(A/B)=P(A and B)/P(B)

P(regular customer/ wine ordered)=$\frac{(0.5*0.7)}{ (0.5*0.7)+(0.4*0.5)+(0.1*0.3)}$

=$\frac{0.35}{0.58}$ = 0.6034

III)If wine is ordered, what is the probability that the person ordering is an occasional customer:

P(occasional customer/ wine ordered)= $\frac{0.4*0.5}{(0.5*0.7)+(0.4*0.5)+(0.1*0.3)}$

=0.3448