In the current tax year, IRS estimates that 5% of the millions of individual tax returns would be fraudulent. That is they will contain errors that are purposely made to cheat the government. Although these errors are often well concealed, let's suppose that a thorough IRS audit will uncover them.
(a) If a random 100 tax returns are audited what is the probability that exactly 5 fraudulent returns will be uncovered?
(b) If a random 250 tax returns are audited, what is the probability that the IRS will uncover at least 15 fraudulent returns?
(c) If a random 250 tax returns are audited, what is the probability that the IRS will uncover at least 15 fraudulent returns but at most 20 fraudulent returns?
(d) What is the probability that out of the 250 randomly selected tax returns no fraudulent return is uncovered?