Math 227 - Statistics » Spring 2023 » 06P Complements, Conditional Probability, and Bayes Theorem

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Question #1
A study conducted at a certain college shows that 36% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. Assume that the sample is taken with replacement. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   92.4
B.   88.4
C.   90.4
D.   95.6
Question #2
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant / A / B / C / D Order Accurate / 26 / 4 / 6 / 36 Order Not Accurate / 33 / 24 / 31 / 36 If one order is selected, find the probability of getting an order from Restaurant C given the order that is accurate. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   5.66
B.   8.33
C.   9.11
D.   7.33
Question #3
At Sally's Hair Salon there are three hair stylists. 30% of the hair cuts are done by Chris, 34% are done by Karine, and the rest are done by Amy. Chris finds that when he does hair cuts, 2% of the customers are not satisfied. Karine finds that when she does hair cuts, 8% of the customers are not satisfied. Amy finds that when she does hair cuts, 9% of the customers are not satisfied. Suppose that a customer leaving the salon is selected at random. If the customer is not satisfied, what is the probability that their hair was done by Amy? Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   46.78
B.   49.39
C.   43.46
D.   54.16

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