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 both is 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. What is the probability that a randomly chosen customer both does not order a vegetarian meal and is not a student?
d. Are the events "customer orders a vegetarian meal" and "customer is a student" independent?
e. Are the events "customer orders a vegetarian meal" and "customer is a student" mutually exclusive?
f. Are the events "customer orders a vegetarian meal" and "customer is a student" collectively exhaustive?