Question

The IRS has a group of 45 tax returns, 15 of which contain errors. An IRS auditor randomly selects 3 tax returns from this group. What is the probability the auditor selects none of those containing errors? Round to four decimal places.

Answer 1

Answeeeeeerrrrr

0.2861

Answer 2

Out of 45, there are 45-15=30 that do not contain errors.

If the auditor randomly selects 3 returns, without replacement, then
P(1)=30/45,
for the second one, there will be 29 correct returns out of 44, so
P(2)=29/44
Similarly,
P(3)=28/43
Therefore, by the multiplication rule, the probability of selecting 3 correct returns is the product
P(1)*P(2)*P(3)=30*29*28/(45*44*43)=406/1419