Alison Bender works for an accounting firm. To make sure her work does not contain errors, her manager randomly checks on her work. Alison recently filled out 12 income tax returns for the company's clients. Unknown to anyone, two of these 12 returns have minor errors. Alison's manager randomly selects three returns from these 12 returns. Find the probability that (a) Fewer than 2 of them contains errors

Alison Bender and Income Tax Returns

The probability that fewer than 2 of the returns contains errors is:

8.333%

Step-by-step explanation:

a) Data and Calculations:

Number of income tax returns filed by Alison = 12

Number of returns with minor errors = 2

Percentage of returns with minor errors = 2/12 = 16.67%

Random sampling of returns by Alison's manager = 3/12 = 25%

Fewer than 2 = 1

The probability of 1 error in 12 returns = 1/12 = 0.08333

= 8.333%

b) Since Alison's manager randomly selects three returns from the 12 to check for errors, the probability of discovering the errors is 25% (3/12).  However, the probability that less than 2 contains errors = 8.333% (1/12).

answer: the common difference is -0.10