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There are three blue marbles, three red marbles, and three yellow marb

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There are three blue marbles, three red marbles, and three yellow marb [#permalink]

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New post 19 Dec 2016, 09:41
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There are three blue marbles, three red marbles, and three yellow marbles in a bowl. What is the probability of selecting a yellow marble from the bowl on each of three successive draws from the bowl?

A. 2/243
B. 1/27
C. 1/84
D. 2/9
E. 5/21
[Reveal] Spoiler: OA

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Re: There are three blue marbles, three red marbles, and three yellow marb [#permalink]

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New post 19 Dec 2016, 10:36
\(\frac{3}{9} * \frac{2}{8} * \frac{1}{7} = \frac{1}{3} * \frac{1}{4} * \frac{1}{7} = \frac{1}{84}\)

or

\(\frac{3C3}{9C3} = \frac{1}{84}\)

Answer C

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Bunuel wrote:
There are three blue marbles, three red marbles, and three yellow marbles in a bowl. What is the probability of selecting a yellow marble from the bowl on each of three successive draws from the bowl?

A. 2/243
B. 1/27
C. 1/84
D. 2/9
E. 5/21


We are given that there are three blue marbles, three red marbles, and three yellow marbles in a bowl and need to determine the probability of drawing a yellow marble on each of three draws.

On the first draw, since there are 3 yellow marbles and 9 total marbles, there is a 3/9 chance that a yellow marble will be selected. Next, since there are 2 yellow marbles and 8 total marbles left, there is a 2/8 chance a yellow marble will be selected. Finally, since there is 1 yellow marble and 7 total marbles left, there is a 1/7 chance that a yellow marble will be selected.

Thus, the total probability is:

3/9 x 2/8 x 1/7 = 1/3 x 1/4 x 1/7 = 1/84

Answer: C
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Re: There are three blue marbles, three red marbles, and three yellow marb [#permalink]

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New post 07 Aug 2017, 04:33
shouldn't it be explicitly mentioned in the question "without replacement" or is it understood in all gmat questions?

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New post 07 Aug 2017, 05:31
HARSHI2211 wrote:
shouldn't it be explicitly mentioned in the question "without replacement" or is it understood in all gmat questions?


No, it is not understood - any question like this must tell you if the selections are made with or without replacement, so that should have been mentioned here.
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Re: There are three blue marbles, three red marbles, and three yellow marb [#permalink]

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New post 07 Aug 2017, 06:59
Bunuel wrote:
There are three blue marbles, three red marbles, and three yellow marbles in a bowl. What is the probability of selecting a yellow marble from the bowl on each of three successive draws from the bowl?

A. 2/243
B. 1/27
C. 1/84
D. 2/9
E. 5/21


Favourable cases = 3 yellow out of 3 yellow = 3C3

Total cases = 3 out of 9 = 9C3

Probability = 3C3 / 9C3 = 1/84

ANswer: Option C
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Re: There are three blue marbles, three red marbles, and three yellow marb   [#permalink] 07 Aug 2017, 06:59
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