Question

In a campus restaurant it was found that 35% of all customers order vegetarian meals and that 50% of all customers are students. Further, 25% of all customers who are students order vegetarian meals.

a. What is the probability that a randomly chosen customer is both a student and orders a vegetarian meal?

b. If a randomly chosen customer orders a vegetarian meal, what is the probability that the customer is a student?

c. Are the events “customer orders a vegetarian meal” and “customer is a student” statistically independent?

Answer 1

Let us build a distribution table as follows.

	Student (S)	Non-student (NS)	TOTAL
Orders Vegetarian (V)	(25% x 50%) = 12.5%	(35 - 12.5)% = 22.5%	35%
Orders Non-vegetarian (NV)	(50 - 12.5)% = 37.5%	(65 - 37.5)% = 27.5%	65%
TOTAL	50%	(100 - 50)% = 50%	100%

(a) Probability of (Student and Vegetarian) = P(SV) = 12.5% = 0.125

(b) Probability of (Vegetarian is student) = P(S) / P(V) = 12.5% / 35% = 0.3571

(c) P(V) = 35%/100% = 0.35 and P(S) = 50%/100% = 0.5

Probability of (Student and Vegetarian) = P(SV) = 0.125

P(V) x P(S) = 0.35 x 0.5 = 0.175

Since P(SV) $\dpi{80} \neq$ P(V) x P(S), the events are not independent.