Tax returns audited by the IRS. According to the Internal

Step 1 of 5:

Given 1 in 100 if your income less than  $1 million and 9 in 100.

Then 9 in 100 if your income is $1 million or more.

We consider,

Taxpayer is audited : A

Taxpayer has income less than $1 million : B and

Taxpayer has income of $1 million or higher : C

Our goal is :

a). We need to find the probability that a taxpayer with income less than $1 will be audited by the

IRS, with income $1 million or more.

b). We need to find the probability that exactly one will be audited.

c). We are repeating part (b) assuming that 5 taxpayers with income of $1 million or more are randomly selected.

d). We need to find the probability that none of these taxpayers will be audited by the IRS.

e). We need to find what assumption did you have to make in order to answer these questions using the methodology presented in this section.

a). Now we have to find the probability that a taxpayer with income less than $1 will be audited by the IRS, with income $1 million or more.

Now the probability of A given B is

\(\begin{array}{l}\mathrm{P}(A / B)=\frac{1}{100} \\ \mathrm{P}(A / B)=0.01\end{array}\)

Therefore, P(A/B) = 0.01.

Then the probability of A given C is

\(\begin{array}{l}\mathrm{P}(A / C)=\frac{9}{100} \\ \mathrm{P}(A / C)=0.09\end{array}\)

Therefore, P(A/C) = 0.09.