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# Only one of ten pens in a box is defective. Three pens are randomly dr

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Math Expert
Joined: 02 Sep 2009
Posts: 64163
Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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18 Apr 2018, 17:23
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Difficulty:

15% (low)

Question Stats:

73% (00:47) correct 27% (01:35) wrong based on 106 sessions

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Only one of ten pens in a box is defective. Three pens are randomly drawn from the box, one at a time. If none of those three pens is defective, what is the probability that the next pen randomly drawn is defective?

(A) 1/10
(B) 1/7
(C) 7/10
(D) 6/7
(E) 9/10

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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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19 Apr 2018, 16:49
1
As the number of pens in the box after 3 withdrawal is 7, and defective pen remaining in the box is still 1. Probability of getting defective pen in 4th draw = 1/7

In this question, I don't think any reason to put back the pen back into the box again.
But if the pens are put back in the box, we get probability = 1/10, since the total number of pens in the box would be 10.

urvashis09 wrote:
I think it might help to have the information whether the pen drawn is put back into the box. That is, are the events independent?

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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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20 Apr 2018, 01:01
1
You got it right...
If nothing is written, it means without replacement.

urvashis09 wrote:
gmatbusters wrote:
As the number of pens in the box after 3 withdrawal is 7, and defective pen remaining in the box is still 1. Probability of getting defective pen in 4th draw = 1/7

In this question, I don't think any reason to put back the pen back into the box again.
But if the pens are put back in the box, we get probability = 1/10, since the total number of pens in the box would be 10.

urvashis09 wrote:
I think it might help to have the information whether the pen drawn is put back into the box. That is, are the events independent?

Are we supposed to assume "without replacement" if nothing is mentioned in the question stem?

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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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18 Apr 2018, 18:11
Was: 9 non-defective + 1 defective = 10
Minus: 3 non-defective
Now: 6 non defective + 1 defective = 7

Probability to get 1 defective = 1/7

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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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19 Apr 2018, 11:27
I think it might help to have the information whether the pen drawn is put back into the box. That is, are the events independent?
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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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20 Apr 2018, 00:50
gmatbusters wrote:
As the number of pens in the box after 3 withdrawal is 7, and defective pen remaining in the box is still 1. Probability of getting defective pen in 4th draw = 1/7

In this question, I don't think any reason to put back the pen back into the box again.
But if the pens are put back in the box, we get probability = 1/10, since the total number of pens in the box would be 10.

urvashis09 wrote:
I think it might help to have the information whether the pen drawn is put back into the box. That is, are the events independent?

Are we supposed to assume "without replacement" if nothing is mentioned in the question stem?
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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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27 Mar 2019, 04:55
Can someone please give a mathematical explanation of the answer, with steps?
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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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27 Mar 2019, 09:43
Bunuel wrote:
Only one of ten pens in a box is defective. Three pens are randomly drawn from the box, one at a time. If none of those three pens is defective, what is the probability that the next pen randomly drawn is defective?

(A) 1/10
(B) 1/7
(C) 7/10
(D) 6/7
(E) 9/10

total pens = 10
so first three pens are taken out
left with 7 pens
since only 1 pen is defective so P = 1/7
IMO B
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Re: Only one of ten pens in a box is defective. Three pens are randomly dr  [#permalink]

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29 Mar 2019, 06:48
Bunuel wrote:
Only one of ten pens in a box is defective. Three pens are randomly drawn from the box, one at a time. If none of those three pens is defective, what is the probability that the next pen randomly drawn is defective?

(A) 1/10
(B) 1/7
(C) 7/10
(D) 6/7
(E) 9/10

Since we have 7 pens left after three non-defective pens are drawn, and one of the 7 pens is defective, the probability that the 4th pen drawn is defective is 1/7.

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Re: Only one of ten pens in a box is defective. Three pens are randomly dr   [#permalink] 29 Mar 2019, 06:48