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

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The probability that the IRS auditor selects none of the three tax returns containing errors is calculated by multiplying the probabilities of selecting returns without errors sequentially. The first return has a probability of 30 out of 45 not containing errors, the second has 29 out of 44, and the third has 28 out of 43. This results in a final probability of (2/3)(29/44)(28/43), which can be rounded to four decimal places for precision. Additionally, the probability that a randomly selected tax return contains errors is 15 out of 45, while the probability that it does not contain errors is 30 out of 45. The discussion emphasizes the importance of understanding independent probabilities in this context.
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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.
 
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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.
 
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).
 
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