A bag contains 3 green marbles, three red marbles and 2 blue marbles.

Question

A bag contains 3 green marbles, three red marbles and 2 blue marbles. If 3 marbles are randomly drawn from the bag, what is the probability of selecting 2 red marbles and 1 green marble?

A. 1/336
B. 1/56
C. 3/56
D. 9/56
E. 9/28

Luckisnoexcuse · Answer

Probability is Favorable outcomes/Total outcomes

Total Outcomes = 8C3 = 8*7*6/3*2 = 56

Favorable outcomes = 3C2 * 3C1 = 3*3 = 9

Hence D 9/56

RaguramanS · Answer

3R, 3G, 2B
P(2r, 1g)=  \frac{no of desired outcome}{total outcome} 
Total outcome= 8C3 ( Choosing any 3 from total 8 balls)
Desired outcome= 3C2*3C1
3C2= Choosing 2 red balls from 3 red
3C1= Choosin1 green ball from 3 green

P(2r,1g)= \frac{3C2*3C1}{8C3}  =9/56

GMATinsight · Answer

Availability= 3G 3R 2B
Requirements: 2R 1G

Favourable cases = 3C2*3C1 = 3*3= 9
Total cases = 8C3 = 56

Probability= 9/56

Answer Option D

ScottTargetTestPrep · Answer

We are given that a bag contains 3 green marbles, 3 red marbles, and 2 blue marbles. We need to determine the probability of selecting 2 red marbles and 1 green marble.
 
The red marbles can be selected in 3C2 = 3 ways. The green marble can be selected in 3C1 = 3 ways.
 
The total number of ways to select the three marbles is 8C3 = 8!/ (8 x 7 x 6)/3! = 56.
 
Thus, the probability is (3 x 3)/56 = 9/56. 
 
Answer: D

Sarjaria84 · Answer

Bunuel ,

I was trying to solve this as below, please let me know where I am going wrong.

Probability of selecting 2 red balls and 1 green ball,
= 3/8 x 2/7 x 3/6
= 3/56

Similarly probability of selecting 1 green and 2 red balls
= 3/8 x 3/7 x 2/6 = 3/56

Therefore, probability = 3/56 + 3/56 = 6/56

Thanks
Saurabh

Bunuel · Answer

P(RRG) = 3/8*2/7*3/6*3!/2! = 9/56. We are multiplying by 3!/2! because RRG can occur in several way: RRG, RGR, GRR.

Answer: D

Sarjaria84 · Answer

So I missed solving for RGR selection, another 3/56 which will make total = 9/56

or 3/56*3!/2! = 9/56 (much faster)

Got it, Thanks  Bunuel .

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.

A bag contains 3 green marbles, three red marbles and 2 blue marbles.

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

A bag contains 3 green marbles, three red marbles and 2 blue marbles.

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