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# A leather pouch contains 10 light bulbs, two of which are de

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Senior Manager
Joined: 20 May 2014
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A leather pouch contains 10 light bulbs, two of which are de [#permalink]  29 Oct 2017, 01:18
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Question Stats:

75% (00:39) correct 24% (00:35) wrong based on 33 sessions
A leather pouch contains 10 light bulbs, two of which are defective.

 Quantity A Quantity B The probability of drawing two defective light bulbs (without replacement) The probability of drawing two defective light bulbs (without replacement) and then a non-defective bulb

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for correct solution.
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Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink]  30 Oct 2017, 07:01
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The probability of extracting two defective light bulbs without replacement is equal to $$\frac{2}{10}*\frac{1}{9} = \frac{1}{45}$$.

The probability of extracting two defective light bulbs without replacement and then a non-defective one is equal to $$\frac{2}{10}*\frac{1}{9}*\frac{8}{8} = \frac{1}{45}$$.

The idea is that there are 2 defective light bulbs out of 10 in the first draw, then there is just one out of the 9 light bulbs remained. Once the two defective light bulbs are extracted there are eight out of 8 non defective light bulbs.

The two quantities are equal.

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Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink]  20 Dec 2018, 14:54
10 light bulbs: 8 non-defective + 2 detective
A: The probability of drawing two defective light bulbs (without replacement):
For taking the first one, the probability of being defective is 2/10, for the next one the probability is 1/9, so A equals: 2/10 * 1/ 9 = 2 / 90

B: The probability of drawing two defective light bulbs (without replacement) and then a non-defective bulb:
For taking the first one, the probability of being defective is 2/10, for the next one the probability is 1/9, for the third one, because now we have already taken the two defective lights and there are 8 non-defective lights, the probability of taking a non-defective light is 8/8, so B equals: 2/10 * 1/ 9 * 8/8 = 2 / 90

A and B are equal. The answer is C.
_________________

Re: A leather pouch contains 10 light bulbs, two of which are de   [#permalink] 20 Dec 2018, 14:54
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