FRQ 2 At a particular coffee shop, 92% of customers order a beverage, 3% of customers order food alone (order food and not a beverage), and 12% of customers order food and a beverage. Suppose we randomly select a customer. Let B = the customer orders a beverage and F = the customer orders food.

a) What is P(F)? Interpret this value in context.

b) What is the probability that the customer orders food given that they order a beverage? Write this event in symbolic form and find the probability.

c) If 180 customers are randomly selected, how many of them can we expect to order neither food nor a beverage? Justify your response.

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?