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

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Math Expert
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [0], given: 12778

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

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19 Dec 2016, 08:41
Expert's post
5
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Difficulty:

15% (low)

Question Stats:

77% (00:43) correct 23% (01:01) wrong based on 130 sessions

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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

_________________

Kudos [?]: 139194 [0], given: 12778

Senior Manager
Joined: 13 Oct 2016
Posts: 367

Kudos [?]: 413 [0], given: 40

GPA: 3.98
Re: There are three blue marbles, three red marbles, and three yellow marb [#permalink]

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19 Dec 2016, 09:36
$$\frac{3}{9} * \frac{2}{8} * \frac{1}{7} = \frac{1}{3} * \frac{1}{4} * \frac{1}{7} = \frac{1}{84}$$

or

$$\frac{3C3}{9C3} = \frac{1}{84}$$

Kudos [?]: 413 [0], given: 40

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1820

Kudos [?]: 1044 [1], given: 5

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

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03 Jan 2017, 16:48
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Expert's post
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

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Jeffery Miller

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Kudos [?]: 1044 [1], given: 5

Intern
Joined: 19 Apr 2017
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Kudos [?]: 10 [0], given: 17

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

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07 Aug 2017, 03:33
shouldn't it be explicitly mentioned in the question "without replacement" or is it understood in all gmat questions?

Kudos [?]: 10 [0], given: 17

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1347

Kudos [?]: 2082 [0], given: 6

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

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07 Aug 2017, 04:31
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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Kudos [?]: 2082 [0], given: 6

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

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07 Aug 2017, 05:59
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

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Kudos [?]: 2468 [0], given: 51

Re: There are three blue marbles, three red marbles, and three yellow marb   [#permalink] 07 Aug 2017, 05:59
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