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A certain music store stocks 800 cellos and 600 violas. Of

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A certain music store stocks 800 cellos and 600 violas. Of  [#permalink]

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New post Updated on: 02 Dec 2012, 03:14
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A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 90 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?

A. 3/16,000
B. 1/8,100
C. 3/1,600
D. 1/90
E. 2/45

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Originally posted by gmatpapa on 18 Feb 2011, 02:57.
Last edited by Bunuel on 02 Dec 2012, 03:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Word Problem DS: Probability  [#permalink]

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New post 18 Feb 2011, 04:08
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I couldn't get the answer:

Pick 1 of the 90 cellos from 800 cellos and pick 1 particular viola(the one that was made from the same tree from which the earlier selected cello was made) from 600 violas.
OR
Pick 1 of the 90 violas from 600 violas and pick 1 particular cello(the one that was made from the same tree from which the earlier selected viola was made) from 800 cellos.

(90/800)*(1/600)+(90/600)*(1/800)

2*90/480000

= 3/8000.

Wonder what did I do wrong!!!
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Re: Word Problem DS: Probability  [#permalink]

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New post 18 Feb 2011, 06:14
I'd say that first you pick one of the ninety cellos which are made from wood (probability: 90/800). Afterwards you pick the fitting viola (probability 1/600). By multiplying (90/800) with (1/600) you get (3/1,600). Thus, solution c is correct.

I think the wording is a bit confusing in this question.
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Re: Word Problem DS: Probability  [#permalink]

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New post 18 Feb 2011, 08:00
gmatpapa wrote:
A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 90 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?

[A] 3/16,000
[B] 1/8,100
[C] 3/1,600
[D] 1/90
[E] 2/45


This is basically the same question as this one: probablility-99046.html (also discussed here: junior-58914.html and here: probability-85523.html).

Solution provided by stanford2012 is correct: 90/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=90/800*1/600=3/16,000.

Answer: A.
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Re: Word Problem DS: Probability  [#permalink]

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New post 12 Nov 2011, 17:09
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Total combinations of cello-viola pairs possible = 600 * 800
Combinations of cello-viola pairs = 90
Hence probability of getting these 90 pairs = 90/(600*800)

Ans = A
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Re: Word Problem DS: Probability  [#permalink]

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New post 13 Dec 2011, 06:09
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In the first selection, we have 90 options, but for the second selection we have just one option that matches with the first option. So,

\(P=\frac{90}{800}*\frac{1}{600}=\frac{3}{16000}\)

Notice that the order is not important. That is, \(\frac{90}{600}*\frac{1}{800}\) leads us to the same result.

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Re: Word Problem DS: Probability  [#permalink]

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New post 13 Dec 2011, 09:55
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A is the answer.

Total number of ways of picking up the pair = 90
Total ways of picking up 1 cello and 1 viola = 800*600

Thus, the probability of picking up a pair from the whole group = (Ways to pick up the pair) / (Ways to pick up 1 cello and 1 viola)
Probability = 90 / (800*600) = 3 / 16000 -> Choice A
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Re: Word Problem DS: Probability  [#permalink]

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New post 02 Dec 2012, 00:42
How many ways to select a paired cello from 800 cello? 90
How many ways to select its pair from the 600 violas? 1

\(\frac{90*1}{800*600}\)
\(\frac{90}{480000}\)
\(\frac{9}{48000}\)
\(\frac{3}{16,000}\)

Answer: 3/16,000
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Re: A certain music store stocks 800 cellos and 600 violas. Of  [#permalink]

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Re: A certain music store stocks 800 cellos and 600 violas. Of &nbs [#permalink] 03 Nov 2018, 06:29
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