Question

tax returns filed manually have a 20% chance of containing errors, while tax returns filed electronically have a 0.05% chance of containing the same. if 2.7 million tax returns are filed each way, how many more erroneous manually filed returns will there be than erroneous electronically filed returns?
○ 270,675
○ 538,650
○ 541,350
○ 269,325

Explanation:

Step1: Calculate erroneous manual returns

First, find the number of erroneous manually filed returns. The number of manual returns is 2.7 million (2,700,000) and the error rate is 20% (0.2). So, we calculate $2,700,000\times0.2$.
$2,700,000\times0.2 = 540,000$

Step2: Calculate erroneous electronic returns

Next, find the number of erroneous electronically filed returns. The number of electronic returns is also 2.7 million (2,700,000) and the error rate is 0.05% (0.0005). So, we calculate $2,700,000\times0.0005$.
$2,700,000\times0.0005 = 1,350$

Step3: Find the difference

Now, find the difference between the number of erroneous manual returns and erroneous electronic returns. Subtract the number of electronic erroneous returns from the manual ones: $540,000 - 1,350$.
$540,000 - 1,350 = 538,650$

Answer:

538,650