Question

An IRS auditor randomly selects 3 tax returns (without replacement) from 45 returns of which 15 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.

Answer 1

The probability that the auditor selects none of the tax returns containing errors is approximately 0.2718.

Step-by-step explanation:

To find the probability that the auditor selects none of the tax returns containing errors, we need to calculate the probability of selecting a non-error return on each of the three selections. Since there are 45 returns in total and 15 of them contain errors, there are 30 non-error returns. So the probability of selecting a non-error return on the first selection is 30/45.

After the first selection, there are 44 returns remaining, with 29 non-error returns. So the probability of selecting a non-error return on the second selection is 29/44.

Finally, after the second selection, there are 43 returns remaining, with 28 non-error returns. So the probability of selecting a non-error return on the third selection is 28/43.

To find the overall probability, we multiply the probabilities of each selection: (30/45) * (29/44) * (28/43) ≈ 0.2718.