Question

Caffe Nero wants to estimate customer preferences. The store conducts a special experiment to determine the preferences of the students in OPER 318 class with its assortment over a period of three days. - On day 1, the store sells only tea (T) and suppose it observes that 90% of the students in OPER 318 class buy tea, 10% of them buy nothing. - On day 2, the store sells only coffee (C) and suppose it observes that 90% of the students in the class buy coffee, 10% of them buy nothing. - On day 3, the store sells both tea and coffee. Suppose it observes that 30% of the students in the class buy tea, 60% of them buy coffee, and 10% buy nothing. Estimate the values of α, i.e., the proportion of customers for each type in OPER 318 class.

Possible Types	α
(C)	?
(T)	?
(C,T)	?
(T,C)	?
O	?

Answer 1

Solution:

Given that

On day 1, the store sells only tea (T)

suppose it observes that 90% of the students

On day 2, the store sells only coffee (C)

suppose it observes that 90% of the students in the class buy coffee, 10% of them buy nothing.

On day 3, the store sells both tea and coffee

Suppose it observes that 30%