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

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

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New post 27 Mar 2013, 07:17
3
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A
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C
D
E

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  35% (medium)

Question Stats:

63% (01:16) correct 37% (01:18) wrong based on 260 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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Re: What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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New post 28 Mar 2013, 06:01
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summer101 wrote:
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%
(2) The probability that there is more than 1 defective pen in the box is 3%


Total probability = Probability that there are no defective pen boxes +probability that there is exactly 1 defective pen boxes+ probability that there are more than 1 defective pen boxes

STAT1
tells us about the number of non defective pen boxes.. but we dont have any information about the number of more than 1 defective pen boxes
So, Its NOT SUFFICIENT

STAT2
tells us about the number of more than 1 defective pen boxes but does not tell us about the number of non defective pen boxes..
So, Its NOT SUFFICIENT

Taking both together we have both the information we were looking for
the number of non defective pen boxes and
the number of more than 1 defective pen boxes

So, we have
total probability = 1 = Probability that there are no defective pen boxes +probability that there is exactly 1 defective pen boxes+ probability that there are more than 1 defective pen boxes
1= .96 + probability that there is exactly 1 defective pen boxes + .3
so, probability that there is exactly 1 defective pen boxes = .1 = 1%

So, answer will be C
Hope it helps!
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Re: What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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New post 13 Sep 2016, 08:34
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Hi,

Just for discussion- is "Probability that there are no defective pens in box" same as "The probability that all the pens in the box are not defective is 96%". Would you want to throw more light on that? Calculation looks justified and I got the same answer as well but would like to discuss on that.

Bunuel,

Your thoughts please. Can you explain in a different way?

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

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New post Updated on: 25 Oct 2017, 03:57
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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, 03:19.
Last edited by saswata4s on 25 Oct 2017, 03:57, edited 1 time in total.
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Re: What is the probability that there is exactly 1 defective pen in a box  [#permalink]

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New post 25 Oct 2017, 03:55
(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

Answer 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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Re: What is the probability that there is exactly 1 defective pen in a box   [#permalink] 13 Aug 2019, 10:06
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