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

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Bunuel
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What is the probability that there is exactly 1 defective pen in a box [#permalink] New post   30 Apr 2020, 02:02
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E

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60% (01:22) correct 40% (01:21) wrong based on 105 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] New post   30 Apr 2020, 02:23
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Since it is pretty clear that all the values are given in percents, there is no way to determine the avg number of defective pens per box.
Statement 1:Each box contains 100 pens.
Statement 2:Each box contains 1,000,000 pens.
Clearly the average number of pens in statement 1 will be less than the average number of pen in statement 2.
Both the statements are not sufficient alone and even after combining.
Hence E should be the right answer.

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Re: What is the probability that there is exactly 1 defective pen in a box [#permalink] New post   30 Apr 2020, 02:37
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Q. 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.

96% there are 0 defective, the other 4% must have 1 or more defective pens. We don't know exactly how the 4% is distributed yet.
NOT SUFFICIENT

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

3% there are 2 or more defective, the other 97% must have 0 or 1 defective pen. We don't know exactly how the 97% is distributed yet.
NOT SUFFICIENT

Combined

96% there are 0 defective, while the other 3% are 2 or more defective pens. As a result, 1% there are exactly 1 defective pen.
SUFFICIENT

FINAL ANSWER IS (C)

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Re: What is the probability that there is exactly 1 defective pen in a box [#permalink] New post   30 Apr 2020, 19:31
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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.
1) p(~ def)=0.96
p(def)=0.04
not sufficient
2)p(> 1 def)=0.03
not sufficient
1+2)
p(exactly 1 def)=p(def)-p(>1 def)
sufficient
Ans C
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Re: What is the probability that there is exactly 1 defective pen in a box [#permalink] New post   20 Jul 2023, 01:58
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Re: What is the probability that there is exactly 1 defective pen in a box [#permalink]
20 Jul 2023, 01:58
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