In the current tax year, IRS estimates that 5% of the many high net worth 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.

If at random 100 such tax returns are audited, what is the probability that exactly 5 fraudulent returns will be uncovered?

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If at random 200 such tax returns are audited, what is the probability that at least 15 fraudulent returns will be uncovered?

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If at random 140 such tax returns are audited, what is the probability that at the most 11 fraudulent returns will be uncovered?