a customer is randomly selected from a coffee shop.Let a be the event the select

Question

a customer is randomly selected from a coffee shop.Let a be the event the selected customer orders beverage and b the event the customer ordered food. suppose P(a) = .65, P(b) = .45 and P( a or b) = .98

a. What is the probability that a customer did not order food nor beverage?

b. What is the probability that the customer ordered food and beverage?

c. What is the probability the customer ordered a beverage but not food? ( hint, use answer from part b)

d. are the events a and b mutually exclusive?

Explanation / Answer

a) Probability that a customer did not order food nor beverage

= 1 - P(a or b) = 1 - 0.98 = 0.02

Therefore 0.02 is the required probability here.

b)

P(a) = 0.65, P(b) =0.45 and P(a or b ) = 0.98

Therefore using addition law of probability we get:

P( a or b) = P(a) + P(b) - P(a and b)

0.98 = 0.65 + 0.45 - P(a and b)

Therefore we get:

P(a and b) = 0.98 - 0.65 - 0.45 = 0.12

Therefore 0.12 is the required probability here.

c) Probability the customer ordered a beverage but not food:

= P(a) - P( a and b) = 0.65 - 0.12 = 0.53

Therefore 0.53 is the required probability here.

d) For mutually exclusive events, P( a and b ) should be equal to 0, which is not the case therefore a and b are not mutually exclusive events.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.