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

Question

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probability of selecting exactly one blue marble and two red marbles from the bowl after three successive marbles are withdrawn from the bowl?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

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

vitaliyGMAT · Accepted Answer

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

Bunuel · Answer

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:

Combinatorics Made Easy!

Theory on Combinations

DS questions on Combinations 
 PS questions on Combinations

Tough and tricky questions on Combinations

Probability Made Easy!

Theory on probability problems

Data Sufficiency Questions on Probability 
 Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.

iqahmed83 · Answer

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I don't quite understand this part of the question "after three successive marbles are withdrawn from the bowl?"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

Bunuel · Answer

It means that 3 marbles were taken from the bowl one by one.

JeffTargetTestPrep · Answer

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.

Answer: B

GyMrAT · Answer

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

Answer B.

Thanks,
GyM

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards