# What is the probability that she selects none of those containing errors

#### rainbow

##### New member
A IRS auditor randomly selects 3 tax returns 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.

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
What is the probability that a randomly selected tax return contains errors? Does not contain errors?

Since the presence of errors in different returns is presumably independent, the probability of no errors in three reports is the product of the corresponding probabilities for each report.

#### Country Boy

##### Well-known member
MHB Math Helper
Initially there are 45 returns. 15 of them contain errors. 45- 15= 30 do not contain errors. The probability the first selected does not contain errors is 30/45= 2/3. If the first selected contains errors, where are then 44 returns 29 of which contain errors. The probability the second return also does not contain errors is 29/44. If the second selected also does not contain errors then there are 43 returns 28 of which do not contain errors. The probability the third return does not contain errors is 28/43. The probability the three selected returns do not contain errors is (2/3)(29/44)(28/43).