An accounting firm uses sampling methods in its client auditing processes. Accounts of a particular type are grouped together in a batch size of 25. The auditor is concerned about erroneous accounts escaping the auditing process. Sampling and auditing the accounts is time consuming and very expensive, and a random sample of size n = 5 is about the largest sample that can practically be used.

(a) Suppose that the batch of accounts contains one erroneous account. What is the probability that the sample that is selected contains the erroneous account?

(b) Suppose that the batch now contains two erroneous accounts. What is the probability that the sample that is selected contains an erroneous account?

(c) How many erroneous accounts must be in the batch of accounts for a random sample of size n = 5 to have a probability of at least 0.50 containing the erroneous account?