Answer:
(A) The odds that the taxpayer will be audited is approximately 0.015.
(B) The odds against these taxpayer being audited is approximately 65.67.
Step-by-step explanation:
The complete question is:
Suppose the probability of an IRS audit is 1.5 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.
A. What are the odds that the taxpayer will be audited?
B. What are the odds against such tax payer being audited?
Solution:
The proportion of U.S. taxpayers who were audited is:
P (A) = 0.015
Then the proportion of U.S. taxpayers who were not audited will be:
P (A') = 1 - P (A)
= 1 - 0.015
= 0.985
(A)
Compute the odds that the taxpayer will be audited as follows:
[tex]\text{Odds of being Audited}=\frac{P(A)}{P(A')}[/tex]
[tex]=\frac{0.015}{0.985}\\\\=\frac{3}{197}\\\\=0.015228\\\\\approx 0.015[/tex]
Thus, the odds that the taxpayer will be audited is approximately 0.015.
(B)
Compute the odds against these taxpayer being audited as follows:
[tex]\text{Odds against Audited}=\frac{P(A')}{P(A)}[/tex]
[tex]=\frac{0.985}{0.015}\\\\=\frac{3}{197}\\\\=65.666667\\\\\approx 65.67[/tex]
Thus, the odds against these taxpayer being audited is approximately 65.67.
