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14.02.2020 •
Mathematics
Five Cs Bank issues credit cards to its customers. In the past 3.4% of the out-of-state nonfraudulent credit card transactions were made at gasoline stations and 9.2% of the out-of-state fraudulent credit card transactions were made at gasoline stations. Based on historical transactions 97.7% of out-of-state credit card transactions are legitimate while the rest of its out-of-state credit card transactions are fraudulent. An out-of-state credit card transaction took place at a gasoline station, what is the probability the transaction is fraudulent?
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Ответ:
0.0838 (8.62%)
Step-by-step explanation:
defining the event G= an out-of-state transaction took place in a gasoline station , then the probability is
P(G) = probability that the transaction is fraudulent * probability that took place in a gasoline station given that is fraudulent + probability that the transaction is not fraudulent * probability that took place in a gasoline station given that is not fraudulent = 0.033 * 0.092 + 0.977 * 0.034 = 0.0362
then we use the theorem of Bayes for conditional probability. Defining also the event F= the transaction is fraudulent , then
P(F/G)=P(F∩G)/P(G) = 0.033 * 0.092 /0.0362 = 0.0838 (8.62%)
where
P(F∩G)= probability that the transaction is fraudulent and took place in a gasoline station
P(F/G)= probability that the transaction is fraudulent given that it took place in a gasoline station
Ответ:
Step-by-step explanation:
let F = fraud credit card transaction and G = legit credit card transactionC =credit card transaction at gasoline stationP(G) = 0.977P(F) = 1 - P(G) = 0.023P(C|G) = 0.034P(C|F) = 0.092To find what is the probability the transaction is fraudulent = P(F|C)
From application of baye's rule ;
P(F|C) = P(F) P(C|F) / P(F) P(C|F) + P(G) P(C|G)
= 0.092 X 0.023 / 0.023 X 0.092 + 0.097 X 0.034
= 0.0599 is the probability the transaction is fraudulent
Ответ:
58 stamps is the number she gets each week. So if she went for one week, 58*1=58. 58*2=116 and so on. Because we don't know the exact number of weeks, we say 58w or 58*w because you multiply however many number of weeks she collects.