According to the Internal Revenue Service (IRS), the chances of your tax return being audited are about 1 in 100 if your income is less than $1 million and 9 in 100 if your income is $1 million or more (IRS Enforcement and Services Statistics).
a. What is the probability that a taxpayer with income less than $1 million will be audited by the IRS? With income $1 million or more?
b. If five taxpayers with incomes under $1 million 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 $1 million or more are randomly selected.
d. If two taxpayers with incomes under $1 million are randomly selected and two with incomes more than $1 million 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?