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# What is the probability that there is exactly 1 defective pen in a box

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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24 Oct 2017, 22:54
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:12) correct 28% (01:29) wrong based on 65 sessions

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What is the probability that there is exactly 1 defective pen in a box of pens?

(1) The probability that all the pens in the box are not defective is 96 percent.
(2) The probability that there is more than 1 defective pen in the box is 3 percent.

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What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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Updated on: 25 Oct 2017, 02:57
1
Question: probability of exactly 1 defective pen in the box = ?

(1) The probability that all the pens in the box are not defective is 96 percent:

In this case, we can say that the probability of atleast 1 pen is defective = 4%
But we cant not say the probability of exactly 1 pen is defective. Hence, Insuff.

(2) The probability that there is more than 1 defective pen in the box is 3 percent:

In this case, we can say that the probability of atmost 1 pen is defective = 100 - 3 = 97%
However, this includes = the probability of 1 pen is defective + the probability of no pen is defective. Hence, insuff.

(1) & (2) together,
from 2: probability of atmost 1 pen is defective = 97%
from 1: probability of all the pens are not defective = 96%

Hence, probability of exactly1 pen is defective = 97-96 = 1%
Ans: C
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Originally posted by saswata4s on 25 Oct 2017, 02:19.
Last edited by saswata4s on 25 Oct 2017, 02:57, edited 1 time in total.
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Joined: 02 Jun 2009
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Location: India
Concentration: Technology, General Management
Re: What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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25 Oct 2017, 02:29
According to the explanation above answer should be c

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Re: What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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25 Oct 2017, 02:55
(1) 4% of probability that either 1 pen or more are edefective
(2) 97% of probability that either 1 pen or none are defective
(1)+(2)
96%=0
97%=1+0
1%=1 pen

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Joined: 27 May 2014
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Re: What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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25 Oct 2017, 03:00
nitimohan wrote:
According to the explanation above answer should be c

Sent from my SM-A700FD using GMAT Club Forum mobile app

Thanks for pointing out. Sorry for the typo, corrected now .
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Re: What is the probability that there is exactly 1 defective pen in a box &nbs [#permalink] 25 Oct 2017, 03:00
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