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28 August, 16:27

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.

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  1. 28 August, 16:36
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    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
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