The Millennium Restaurant serves a choice of rice, baked potato or French fries
ID: 3201381 • Letter: T
Question
The Millennium Restaurant serves a choice of rice, baked potato or French fries with each of its three entrees. Last month, 1000 customers ate at the restaurant and their selections are given in the following table: a) What is the probability that a customer ordered fish? b) What is the probability that a customer ordered steak given that the customer ordered a baked potato? c) Is the event "customer ordered chicken" independent of the event "customer ordered french fries"? Give a reason for your answer. For the next two parts only, assume that a customer dined at the restaurant twice during the month ordering different entrees on each visit. On the first visit the customer ordered chicken. d) What is the probability that the customer ordered fish on the second visit ? e) What is the complementary event to "the customer ordered fish on the second visit"? What is the probability of this event? For the last 3 paints of the problem, assume that a random customer during the month was actually a restaurant reviewer. The review will be published in next week's issue of Atlanta Magazine. From past experience, it is known that the probability of a bad review is .2 if the reviewer orders chicken, .3 if the reviewer orders fish, and .1 if the reviewer orders steak. f) Draw a fully labeled probability tree for the experiment "reviewer orders entree and writes bad or good review". g) What is the probability that the review will be bad? h) What is the probability that the reviewer had steak given that the review is bad?Explanation / Answer
Solution:-
a) The probability that a costumer ordered fish = 0.20
Number of costumer ordered fish = 200
Total number of costumer = 1000
The probability that a costumer ordered fish = 200/1000 = 0.20
b) The probability that costumer ordered steak given that costumer ordered baked potato is 0.4444.
Number of costumer ordered steak given that costumer ordered baked potato = 200
Number of costumers who has ordered baked patoto = 450
The probability that costumer ordered steak given that costumer ordered baked potato = 200/450 = 0.4444
c) The event costumer ordered chicken is not independent of costumer orderes french fries, beacuse of the total orders 100 times the chicken is ordered when the french fries are ordered.
d) The probability that a costumer ordered fish in second visit = 0.20
If the costumer ordering chicken in the first time it will not have any affect on the second visit.
Number of costumer ordered fish = 200
Total number of costumer = 1000
The probability that a costumer ordered fish on second = 200/1000 = 0.20
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