Question: A fraud detection system at a payment processor has a 90% true positive rate (detected transaction is actually fraud) and a 1% false positive rate

A fraud detection system at a payment processor has a 90% true positive rate (detected transaction is actually fraud) and a 1% false positive rate (detected transaction is not fraud). Over the past year, a review shows that 1460 of 1,000,000 transactions were actually fraudulent.

(a) What is the probability that the fraud detection system signals fraud for a randomly selected transaction?

(b) What is the probability a transaction is fraudulent if the detection signals fraud?

(d) Assuming fraudulent transactions are independent of each other with the constant average rate from (c), what is the probability of observing 0 fraud transactions in a day?

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