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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: 51227
There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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22 Dec 2016, 01:29
3
6
00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:55) correct 35% (01:56) wrong based on 145 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probability of selecting exactly one blue marble and two red marbles from the bowl after three successive marbles are withdrawn from the bowl?

A. 2/81
B. 3/28
C. 2/27
D. 1/28
E. 1/84

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Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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22 Dec 2016, 01:56
1
4
BRR + RBR + RRB

$$\frac{3}{9}*\frac{3}{8}*\frac{2}{7} + \frac{3}{9}*\frac{3}{8}*\frac{2}{7} + \frac{3}{9}*\frac{2}{8}*\frac{3}{7} = \frac{3}{28}$$

or

$$\frac{_3C_1*_3C_2}{_9C_3} = \frac{3}{28}$$

B
##### General Discussion
Intern
Joined: 26 Aug 2016
Posts: 10
Re: There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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02 Jan 2017, 02:25
Hey Bunuel,

Would you be kind enough to explain the answer....I don't quite understand it.
Math Expert
Joined: 02 Sep 2009
Posts: 51227
Re: There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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02 Jan 2017, 04:25
iqahmed83 wrote:
Hey Bunuel,

Would you be kind enough to explain the answer....I don't quite understand it.

Please tell me what is unclear here: there-are-three-blue-marbles-three-red-marbles-and-three-yellow-marb-231053.html#p1780047 Thank you.
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Intern
Joined: 26 Aug 2016
Posts: 10
Re: There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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02 Jan 2017, 04:44
Hey Bunuel,

I don't quite understand this part of the question "after three successive marbles are withdrawn from the bowl?"

I also don't understand the reasoning behind vitaliyGMAT answer....

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 51227
Re: There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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02 Jan 2017, 04:45
iqahmed83 wrote:
Hey Bunuel,

I don't quite understand this part of the question "after three successive marbles are withdrawn from the bowl?"

I also don't understand the reasoning behind vitaliyGMAT answer....

Thanks!

It means that 3 marbles were taken from the bowl one by one.
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Math Expert
Joined: 02 Sep 2009
Posts: 51227
Re: There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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02 Jan 2017, 04:48
1
2
iqahmed83 wrote:
Hey Bunuel,

I don't quite understand this part of the question "after three successive marbles are withdrawn from the bowl?"

I also don't understand the reasoning behind vitaliyGMAT answer....

Thanks!

This is quite an easy probability question, so if you have problems solving it you should go through the basics again. Please check the link s below:

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Tough and tricky questions on Combinations

Theory on probability problems

Data Sufficiency Questions on Probability
Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: There are three blue marbles, three red marbles, and three yellow marb  [#permalink]

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14 Jul 2018, 08:26
Bunuel wrote:
There are three blue marbles, three red marbles, and three yellow marbles in a bowl. What is the probability of selecting exactly one blue marble and two red marbles from the bowl after three successive marbles are withdrawn from the bowl?

A. 2/81
B. 3/28
C. 2/27
D. 1/28
E. 1/84

We are given there are 3 blue marbles, 3 red marbles, and 3 yellow marbles in a bowl. We must determine the probability of selecting one blue and two red marbles in 3 attempts.
On the first draw, since there are 3 red marbles and 9 total marbles, there is a 3/9 chance that a red marble will be selected. Next, since there are 2 red marbles and 8 total marbles left, there is a 2/8 chance a red marble will be selected on the second draw. Finally, when selecting the blue marble, since there are 3 blue marbles and 7 marbles left, there is a 3/7 chance a blue marble will be selected for the final marble. However, there are 3 different ways to select the 2 red and 1 blue marbles:

R - R - B:

R - B - R:

B - R - R:

Note that each of these 3 ways has the same probability of occurring, even though the individual probabilities appear in a different order. Thus, the total probability is:

3 x (3/9 x 2/8 x 3/7) = 3 x (1/3 x 1/4 x 3/7) = 3/28

Alternate Solution:

There are 9C3 = (9 x 8 x 7)/(3 x 2 x 1) = 84 ways to choose 3 marbles from a total of 9 marbles.

There are 3C1 = 3 ways to choose a blue marble and 3C2 = 3 ways to choose a red marble. Thus, there are 3 x 3 = 9 ways to make a selection that involves two red and one blue marble.

Thus, the probability that the selection consists of two red marbles and one blue marble is 9/84 = 3/28.

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

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14 Jul 2018, 10:24
Bunuel wrote:
There are three blue marbles, three red marbles, and three yellow marbles in a bowl. What is the probability of selecting exactly one blue marble and two red marbles from the bowl after three successive marbles are withdrawn from the bowl?

A. 2/81
B. 3/28
C. 2/27
D. 1/28
E. 1/84

Approach 1: Probability of drawing B R R = (3/9)*(3/8)*(2/7)*(3!/2!) = 3/28

Approach 2: Total # of ways of drawing 3 marbles out of 9 marbles = 9C3 =(9*8*7)/(1*2*3) = 3*4*7

# of ways of choosing 1 blue marble out of 3 blue marbles = 3C1 = 3

# of ways of choosing 2 red marbles out of 3 red marbles = 3C2 = 3

Favorable # of ways = 3*3

hence required Probability = 3*3/3*4*7 = 3/28

Thanks,
GyM
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Re: There are three blue marbles, three red marbles, and three yellow marb &nbs [#permalink] 14 Jul 2018, 10:24
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