At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions. Consider a batch of 10 randomly selected suspicious transactions. Suppose the specialist wants to know the probability that 2 of the transactions will be blocked. (i) Define the random variable of interest and state how the variable is distributed. (ii) Find the probability that 2 transactions in the batch will be blocked. Show your work.
At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions. Consider a batch of 10 randomly selected suspicious transactions. Suppose the specialist wants to know the probability that 2 of the transactions will be blocked.
(i) Define the random variable of interest and state how the variable is distributed.
(ii) Find the probability that 2 transactions in the batch will be blocked. Show your work.
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