Question

According to the Internal Revenue Service (IRS), the chances of your tax return being audited are about 6 in 1,000 if your income is less than $50,000; 10 in 1,000 if your income is between $50,000 and $99,999; and 49 in 1,000 if your income is $100,000 or more (Statistical Abstract of the United States: 1995). If two taxpayers with incomes under $50,000 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?

Answer 1

The probability that none of these taxpayers will be audited by the IRS is 0.8996 or 89.36%

Explanation:

According to given:

Probability of being audited for income less than $50,000 = 6/1000 = 0.006

Therefore,

Probability of not being audited for income less than $50,000 = 1 - 0.006 = 0.994

Similary,

Probability of being audited for income more than $100,000 = 49/1000 = 0.049

Therefore,

Probability of not being audited for income more than $100,000 = 1 - 0.049 = 0.951

Now, for the probability of 2 persons with less $50,000 income and 2 persons with more than $100,000 income, to not being audited, we must multiply the probabilities of not being audited of each of the 4 persons.

Therefore,

Probability that none of them is audited = (0.994)(0.994)(0.951)(0.951)

Probability that none of them is audited = 0.8936 = 89.36%