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A box contains 20 bulbs,12 are defective.Four bulbs are selected at

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A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post Updated on: 25 Jun 2015, 05:14
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:53) correct 37% (02:04) wrong based on 131 sessions

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A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12

Originally posted by kanigmat011 on 25 Jun 2015, 05:10.
Last edited by Bunuel on 25 Jun 2015, 05:14, edited 4 times in total.
Renamed the topic and edited the question.
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 25 Jun 2015, 05:11
Totally confused on which approach to be used in order to resolve this
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 25 Jun 2015, 05:19
kanigmat011 wrote:
A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12


12 are defective, 8 not defective.

P(at least one defective out of 4) = 1 - P(none is defective out of 4) = 1 - 8/20*7/19*6/18*5/17 = 955/969.

Answer: D.
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 25 Jun 2015, 05:34
kanigmat011 wrote:
A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12


Bunuel's solution is perfect however another insight to answer the questions is

Since 60% are defective (12/20) therefore the probability of one of the 4 selected bulb defective should be pretty high and should be close to 1

only Option D gives a close enough value as in every other option the probability is even less than 1/2

Answer: Option D
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 25 Jun 2015, 10:02
is this a gmat question ?? looked like some indian exam question !!
Too mch calculations in it..
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 26 Jun 2015, 00:50
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 01 Aug 2015, 05:27
1
kanigmat011 wrote:
A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12


Defective = 12, Not defective = 8

Total possible no. of combinations of 4 = \(20C4\)

Total possible no. of non defective combinations of 4 = \(8C4\) (since only 8 are non defective)

P(none is defective) \(= 8C4/ 20C4 = 14/969\)

P(at least one defective) = 1 - P(none is defective) = \(955/969\)

Answer D
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 01 Aug 2015, 05:42
Probability that at least one of the four bulbs is defective = 1 - (none of the 4 are defective).

Probability that none of the 4 balls are defective = 8C4/20C4 = 70/4845 = 14/969

Probability that at least one is defective = 1 - 14/969 = 955/969. Ans (D).
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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at  [#permalink]

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New post 03 Oct 2018, 16:34
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at &nbs [#permalink] 03 Oct 2018, 16:34
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