Question

A fast-food establishment has many different products for sale. Suppose that the restaurant had

1000 customers in one week, and 650 of those customers ordered a hamburger of some kind, 120 purchased a

milkshake, and 57 ordered both. A customer is selected at random to win a coupon for a free meal. Use the above

information to:

(a) define event A ____________________________ define Aʹ ____________________________

define event B ____________________________ define Bʹ____________________________

define event C ____________________________ define Cʹ____________________________

(b) Find the following probabilities

P(A) _______

P(Bʹ) _______

P(A or B) _______

P(B|A) _______

P(B|Aʹ) _______

P(Aʹ) _______

P(C) _______

P(Aʹ and B) _______

P(A|B) _______

P(B) _______

P(Cʹ) _______

P(A and Bʹ) _______

P(A|Bʹ) _______

Answer 1

a)A=probability of a customer ordering a hamburger

B=probability of a customer ordering milkshake

C=probability of a customer ordering both hamburger and milkshake

b) P(A)=650/1000=0.65

P(B)=120/1000=0.12

P(C)=57/1000=0.057

P(A')=1-P(A)=1-0.65=0.35

P(B')=1-P(B)=1-0.12=0.88

P(C')=1-P(C)=1-0.057=0.943

P(A or B)=P(A)+P(B)-P(A and B)=0.65+0.12-0.057=0.713

P(A' and B)=P(B)-P(A and B)=0.12-0.057=0.063

P(A and B')=P(A)-P(A and B)=0.65-0.057=0.593

P(A|B)=P(A and B)/P(B)=0.057/0.12=0.475

P(B|A)=P(A and B)/P(A)=0.057/0.65=0.088

P(A|B')=P(A and B')/P(B')=0.593/0.88=0.674

P(B|A')=P(A' and B)/P(A')=0.063/0.35=0.18