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A payroll record with an error in it is placed in a filing cabinet wit

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Bunuel
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A payroll record with an error in it is placed in a filing cabinet wit [#permalink] New post   22 Jan 2021, 07:31
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A payroll record with an error in it is placed in a filing cabinet with six error-free payroll records. Two payroll records are randomly selected, without replacement, by an auditor. What is the probability of drawing a corrupted payroll record on the first or the second draw?

A. 1/42
B. 1/21
C. 2/21
D. 1/7
E. 2/7
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Re: A payroll record with an error in it is placed in a filing cabinet wit [#permalink] New post   22 Jan 2021, 07:40
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\(P\)(No Error in both draw)\(=\frac{6}{7}\frac{5}{6}=\frac{30}{42}\)
\(P\)(Error)\(=1-\frac{30}{42}=\frac{12}{42}=\frac{2}{7}\)

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Re: A payroll record with an error in it is placed in a filing cabinet wit [#permalink] New post   24 Jan 2021, 10:35
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Probability of drawing error on 1st draw = 1/7

Probability of drawing error on 2nd draw = 6/7 * 1/6 = 1/7

1/7 + 1/7 = 2/7
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Re: A payroll record with an error in it is placed in a filing cabinet wit [#permalink] New post   26 Jan 2021, 06:49
user9123 wrote:
Probability of drawing error on 1st draw = 1/7

Probability of drawing error on 2nd draw = 6/7 * 1/6 = 1/7

1/7 + 1/7 = 2/7


hey, can you please explain, why on 2nd draw it is multiplied by 1/6 ?
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Re: A payroll record with an error in it is placed in a filing cabinet wit [#permalink] New post   02 Feb 2021, 10:06
Naved24 wrote:
user9123 wrote:
Probability of drawing error on 1st draw = 1/7

Probability of drawing error on 2nd draw = 6/7 * 1/6 = 1/7

1/7 + 1/7 = 2/7


hey, can you please explain, why on 2nd draw it is multiplied by 1/6 ?

6/7 is the probability of six error free payroll and 1/6 is the probability of that 'one' payroll with error.

Why '1/6' ???
Because without replacement means after first payroll is randomly selected from 7(1 error + 6 without error) second is selected from remaining six i.e. the first selected is not replaced in the cabinet to make it seven.
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Re: A payroll record with an error in it is placed in a filing cabinet wit [#permalink]
02 Feb 2021, 10:06
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