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:
![\text{Odds of being Audited}=\frac{P(A)}{P(A')}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20of%20being%20Audited%7D%3D%5Cfrac%7BP%28A%29%7D%7BP%28A%27%29%7D)
![=\frac{0.015}{0.985}\\\\=\frac{3}{197}\\\\=0.015228\\\\\approx 0.015](https://tex.z-dn.net/?f=%3D%5Cfrac%7B0.015%7D%7B0.985%7D%5C%5C%5C%5C%3D%5Cfrac%7B3%7D%7B197%7D%5C%5C%5C%5C%3D0.015228%5C%5C%5C%5C%5Capprox%200.015)
Thus, the odds that the taxpayer will be audited is approximately 0.015.
(B)
Compute the odds against these taxpayer being audited as follows:
![\text{Odds against Audited}=\frac{P(A')}{P(A)}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20against%20Audited%7D%3D%5Cfrac%7BP%28A%27%29%7D%7BP%28A%29%7D)
![=\frac{0.985}{0.015}\\\\=\frac{3}{197}\\\\=65.666667\\\\\approx 65.67](https://tex.z-dn.net/?f=%3D%5Cfrac%7B0.985%7D%7B0.015%7D%5C%5C%5C%5C%3D%5Cfrac%7B3%7D%7B197%7D%5C%5C%5C%5C%3D65.666667%5C%5C%5C%5C%5Capprox%2065.67)
Thus, the odds against these taxpayer being audited is approximately 65.67.