A customer is randomly selected from a coee shop. Let A be the event the selecte
ID: 3221269 • Letter: A
Question
A customer is randomly selected from a coee shop. Let A be the event the selected customer
ordered a beverage, and B be the event the customer ordered food. Suppose P(A) = 0:65; P(B) =
0:45, and P(A [ B) = 0:98.
(a) What is the probability that the customer did not order food nor a beverage?
(b) What is the probability that the customer ordered food and a beverage?
(c) What is the probability the customer ordered a beverage but not food? (Hint: You will use the
answer from part b.)
(d) Are the events of ordering a beverage and ordering food mutually exclusive?
Explanation / Answer
P(A) = 0.65
P(B) = 0.45
P(A | B) = 0.98
or, P(A and B) / P(B) = 0.98
or, P(A and B) = 0.98 * 0.45
or, P(A and B) = 0.44
a) P(customer did not order food nor a beverage) = P(not A and not B)
= 1 - P(A or B)
= 1 - [P(A) + P(B) - P(A and B)]
= 1 - [0.65 + 0.45 - 0.44]
= 0.34
b) P(customer ordered food and a beverage) = P(A and B) = 0.44
c) P(customer ordered a beverage but not food) = P(A and not B)
= P(A) - P(A and B)
= 0.65 - 0.44
= 0.21
d) the events of ordering a beverage and ordering food are not mutually exclusive. Because P(ordering a beverage and ordering food are not mutually exclusive) is not equal to zero.
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