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655-705 Level|   Probability|      
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amanvermagmat
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In a retail shop, 32% pens are defective, and both defective as well 12 Jun 2018, 11:11
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65% (hard)

Question Stats:

54% (01:56) correct 46% (01:39) wrong based on 212 sessions

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In a retail shop, 32% pens are defective, and both defective as well as non-defective pens are identical and kept together so there is no way to tell defective from non-defective. If a customer buys 3 pens randomly, what is the probability that none of the 3 pens will be defective?

(1) If one pen is chosen randomly, the probability of that pen being non-defective is 17/25.

(2) There are total 50 pens in the shop.
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In a retail shop, 32% pens are defective, and both defective as well 12 Jun 2018, 12:01
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In a retail shop, 32% pens are defective, and both defective as well as non-defective pens are identical and kept together so there is no way to tell defective from non-defective. If a customer buys 3 pens randomly, what is the probability that none of the 3 pens will be defective?

(1) If one pen is chosen randomly, the probability of that pen being non-defective is 17/25.

(2) There are total 50 pens in the shop.


>> (2): Sufficient

Total = 50 pens
0.32*50 = 16 defectives
34 Non defectives

Ways of choosing 3 non defective out of 34 fine pieces of pen = 34C3
Ways of choosing 3 out of 50 pieces of pen = 50C3

>>> 34C3 / 50C3 = 374/1225


>> (1): Insufficient

17/25 = 68/100 (hence, 68% are non defective. we know that from the statement)

No information about the total number of pens.


Option B.
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In a retail shop, 32% pens are defective, and both defective as well 21 Jun 2018, 01:58
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just a question. How is the value of total number of pens important for finding out the probability and even percentage can give us the probability.

For me, both the options are sufficient.

Please correct if i am wrong in my concept.
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In a retail shop, 32% pens are defective, and both defective as well 21 Jun 2018, 10:19
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ambujsrv
just a question. How is the value of total number of pens important for finding out the probability and even percentage can give us the probability.

For me, both the options are sufficient.

Please correct if i am wrong in my concept.

see we are given the percentage and not the actual number. we cannot assume the total no. to be 100 even tgough the first statement conforms to that. 17/25 can very well be 68/100 (in which case total pens would be 100) and it can very well be 136/200 (in which case the number of pens is 200).

maybe you thought that in the end we have to get a ratio but actually, the common multiple in the ratio plays a crucial role.
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In a retail shop, 32% pens are defective, and both defective as well 01 Jun 2025, 01:42
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ambujsrv
just a question. How is the value of total number of pens important for finding out the probability and even percentage can give us the probability.

For me, both the options are sufficient.

Please correct if i am wrong in my concept.
we need to know how many pens there are as there is no replacement. Once we get out one pen, the probability of getting another deffective or non deffective pen will no remain the same and will depend on the total number of pens initially.
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