There are three blue marbles, three red marbles ....

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Dec 05, 2017 9:48 am

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

The OA is C.

What are the formulas I should use here? I can find the correct answer. Experts, may you give me some help please?

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Source: Beat The GMAT — Problem Solving | Tue Dec 05, 2017 9:48 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Tue Dec 05, 2017 10:49 am

Hello Vincen.

Let's see what are the formulas here.

We have to pick 1 yellow marble from 3 yellow marbles among 9 total marbles. 3/9=1/3.

Now, we have to pick another yellow marble from 2 yellow marbles among 8 total marbles. 2/8=1/4.

Finally, we have to pick another yellow marble from 1 yellow marble among 7 total marbles. 1/7.

So, the final probability is $$\frac{1}{3}\cdot\frac{1}{4}\cdot\frac{1}{7}=\frac{1}{84}.$$ So, the correct answer is C.

I really hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.

GMAT Prep From The Economist
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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Tue Dec 05, 2017 6:36 pm

This isn't really answerable because it isn't clear if we're replacing the marbles between draws. (It *sounds* like we aren't, but it isn't clear.)

If we ARE replacing the marbles, then it's just ((# of yellow marbles) / (# of marbles))Â³

If we AREN'T replacing the marbles, then it's (# of yellow / total) * ((# of yellow - 1)/(total - 1)) * ((# of yellow - 2)/(total - 2)

So the answer's either 1/27 (replacing) or 1/84 (not replacing). Since both answers are there, I'd say you can burn whatever book this came from.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Oct 11, 2019 2:44 pm

Vincen 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

The OA is C.

What are the formulas I should use here? I can find the correct answer. Experts, may you give me some help please?

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

Scott Woodbury-Stewart
Founder and CEO
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