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There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random

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avenger
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There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink] New post   02 Oct 2007, 13:34
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There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are to be chosen at random and without replacement, what is the probability that both rocks will be slate rocks?

A) 1/3
B) 7/22
C) 1/9
D) 7/66
E) 2/45
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D
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stanford2012
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Re: probability [#permalink] New post   30 Jul 2010, 08:19
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1. Determine probability of chosing first slate rock = number of slate rocks / number of total rocks
=> 15/45 = 1/3

2. Determine probability of selecting second slate rock (note: since we have already chosen one rock and there is no replacement there are only 45 - 1 = 44 rocks left, whereof 14 are slate rocks)
=>14/44

3. Multiply the probabilities of the two selections to determin probability to select two slate rocks in two draws
=> (1/3)*(14/44) = 7/66
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Re: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink] New post   02 Oct 2007, 13:57
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Total No of Rocks = 45

Probability of choosing 1st Slate Rock = 15/45
Probability of choosing 2nd Slate Rock = 14/44 (Without replacement)

So combined probability = 15/45*14/44 = 7/66

So, D.

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Re: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink] New post   04 Oct 2007, 00:39
avenger wrote:
Q34)
There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are to be chosen at random and without replacement, what is the probability that both rocks will be slate rocks?

(a) 1/3
(b) 7/22
(c) 1/9
(d) 7/66
(e) 2/45



15/45 * 14/44 ---> 7/66.

Just add up the total rocks. Then u calculate first prob, then u must subtract the one slate rock from both numerator and denominator.

Ans D.
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Re: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink] New post   04 Oct 2007, 15:53
OA is D.

Thanks guys. At this point I was just blindly guessing due to the time constraints... if i had the time I would have gotten it right...aaarrrgghhh! :-)

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There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink] New post   18 Apr 2016, 11:23
Total no of rocks is 45

Probability of selecting 2 slate rocks ( Of 15 slate rocks ) out of 45 total Rocks is

15C2/45C2

=> 105 / 990

=> 21/198

=> 7/66

Hence answer will be (D) 7/66 :-D :lol:
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Re: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink] New post   12 Oct 2019, 17:12
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avenger wrote:
There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are to be chosen at random and without replacement, what is the probability that both rocks will be slate rocks?

A) 1/3
B) 7/22
C) 1/9
D) 7/66
E) 2/45


The probability of getting two slate rocks is 15/45 x 14/44 = 1/3 x 7/22 = 7/66.

Answer: D
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Re: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink] New post   10 Mar 2024, 09:20
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Re: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks random [#permalink]
10 Mar 2024, 09:20
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