According to the Internal Revenue Service (IRS), the chances of your tax return being audited are about 15 in 1,000 if your income is less than $100,000 and 30 in 1.000 if your income is $100,000 or more (Statistical Abstract of the United States: 1998).

a. What is the probability that a taxpayer with income less than $100,000 will be audited by the IRS? With income $100,000 or more?

b. If five taxpayers with incomes under $100,000 are randomly selected. what is the probability that exactly one will be audited? That more than one will be audited?

c. Repeat part b assuming that five taxpayers with incomes of $100,000 or more are randomly selected.

d. If two taxpayers with incomes under $100,000 are randomly selected and two with incomes more than $100,000 are randomly selected, what is the probability that none of these taxpayers will be audited by the IRS?

e. What assumptions did you have to make in order to answer these questions using the methodology presented in this section?