Question

In 2008, the audit risk for the average individual filing a federal income tax return was about 1 in 100. For individuals with an adjusted gross income of $1 million or higher, the audit risk was about 1 in 16. About 1 in 250 individuals filing federal income tax returns have adjusted gross incomes of$1 million or higher. If an individual income tax return has been chosen to be audited, find the probability that the individual’s adjusted gross income is $1 million or higher.

Solution

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The partition of S:

A1A_{1} = the individual has adjusted tax income of $1\$ 1 milion or more,         P(A1)=1250=0.004P(A_{1})=\displaystyle \frac{1}{250}=0.004\\A2A_{2}= the individual has adjusted tax income less than$1\$1 milion          P(A2)=0.96P(A_{2})=0.96\\\\

We are given:$P(E|A_{1}) =\displaystyle 116\frac{1}{16}=0.0625,         P(E|A_{2}) =1100\frac{1}{100}=0.01

$

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