Question

For the fiscal year 2018 , the IRS audited 2% of individual tax returns with income $200,000 or more. Suppose the percentage stays the same for the current tax year 2019. Express your answer in percentage using 2 decimal places (ex: 0.07%,0.87%, 12.45%,3.90%) 1) Would it be unusual for a return with income of $200.000 or more to be audited? Answer either YES or NO. 2) What is the probability that two randomly selected returns with income of $200,000 or more will be audited? 3) What is the probability that two randomly selected returns with income of $200,000 or more will not be audited? 4) What is the probability that at least one of the two randomly selected returns with income of $200,000 or more will be audited?

Answer 1

It wouldn't be unusual for a return with income of $200,000 or more to be audited. The probability of both being audited is 0.04%, while the probability of neither being audited is 96.04%. The probability of at least one being audited is 3.96%.

Step-by-step explanation:

1) Would it be unusual for a return with income of $200,000 or more to be audited? No, it would not be unusual since 2% is a small but significant proportion.

2) What is the probability that two randomly selected returns with income of $200,000 or more will be audited? The probability is (0.02) × (0.02) = 0.0004 or 0.04%.

3) What is the probability that two randomly selected returns with income of $200,000 or more will not be audited? The probability is (0.98) × (0.98) = 0.9604 or 96.04%.

4) What is the probability that at least one of the two randomly selected returns with income of $200,000 or more will be audited? This can be found by subtracting the probability that neither will be audited from 1: 1 - 0.9604 = 0.0396 or 3.96%.

Answer 2

1) No, it would not be unusual for a return with income of $200,000 or more to be audited. 2) The probability that two randomly selected returns with income of $200,000 or more will be audited is 0.04%. 3) The probability that two randomly selected returns with income of $200,000 or more will not be audited is 99.96%.

Step-by-step explanation:

1) No, it would not be unusual for a return with income of $200,000 or more to be audited. The IRS audits 2% of individual tax returns with income $200,000 or more for both the fiscal year 2018 and the current tax year 2019.

2) The probability that two randomly selected returns with income of $200,000 or more will be audited is the product of the probabilities of each return being audited. Since the percentage stays the same at 2%, the probability is (2/100) * (2/100) = 0.0004, or 0.04%.

3) The probability that two randomly selected returns with income of $200,000 or more will not be audited is the complementary probability of them being audited. That is, 1 - 0.0004 = 0.9996, or 99.96%.

4) The probability that at least one of the two randomly selected returns with income of $200,000 or more will be audited can be calculated using the complementary probability. The probability that none of the returns are audited is 0.9996. So, the probability that at least one of the returns is audited is 1 - 0.9996 = 0.0004, or 0.04%.