Question

One in 104 individual tax returns will be randomly selected to be audited by the IRS. Determine (a) The probability that an individual tax return will be audited. (b) The odds against an individual tax return being audited.

Solution

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Step 1

1 of 2

a.) The probability that an individual tax return will be audited is

P(audited individual tax return)=1104P(audited~individual~tax~return)=\dfrac{1}{104}

b.) Since P(audited individual tax return)=1104P(audited~individual~tax~return)=\dfrac{1}{104}, then

P(not audited individual tax return)=11104=103104P(not~audited~individual~tax~return)=1-\dfrac{1}{104}=\dfrac{103}{104}

Thus, the odds against an individual tax return being audited is given by:

P(not audited individual tax return)P(audited individual tax return)=1031041104=1031,\dfrac{P(not~audited~individual~tax~return)}{P(audited~individual~tax~return)}=\dfrac{\dfrac{103}{104}}{\dfrac{1}{104}}=\dfrac{103}{1}, or 103:1103 : 1

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