A bag contains 12 red marbles. If someone were to remove 2 marbles fro

Question

A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 16/25. How many marbles are in the bag?

A. 24
B. 48
C. 60
D. 72
E. 84

A. 24
B. 48
C. 60
D. 72
E. 84

CareerGeek · Accepted Answer

Red marbles = 12
Let the number of non red marbles = n
--> total marbles in the bag = n + 12
Prob. of picking a non red marble =  \frac{n}{(n + 12)}

Prob that none of the 2 marbles are red =  \frac{n}{(n + 12)} * \frac{n}{(n + 12)} 
-->  \frac{n^2}{(n + 12)^2}  =  \frac{16}{25}  (Given)
-->  \frac{n}{(n + 12)}  =  \frac{4}{5} 
--> 5n = 4n + 48
--> n = 48

Total marbles in the bag = n + 12 = 60

IMO Option C

Pls Hit Kudos if you like the solution

JBN96 · Answer

16/25=(4/5)*(4/5) so 12=1/5 of the total bag.
12*5=60
Quick and easy

Posted from my mobile device

Lampard42 · Answer

Let total marbles be N; So probability of neither marble being Red is  * =16/25 as they are replaced after picking.

So sub answer choices to arrive at the answer; Option C (48/60)*(48/60)=16/25

Archit3110 · Answer

total red = 12
and not red = x
so total marbles = 12+x
now given P of not red two marbles ;
(x/12+x)^2 = 16/25
x/x+12 = 4/5
solve for x = 48 
so total 48+12 = 60
IMO C

tyildirim92 · Answer

Replace the first marble with what? What if it is replaced with a red marble? I guess the wording is wrong.  Bunuel

Posted from my mobile device

Bunuel · Answer

Yes, the wording is not perfect but what the question means that the first marble after it was picked is put back.

rvgmat12 · Answer

Let n be the total number of marbles

((n-12)/n)^2= 16/25

(n-12)/n=4/5

5n-60 = 4n

n= 60

C.

Hope it helps

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 12 red marbles. If someone were to remove 2 marbles fro

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 12 red marbles. If someone were to remove 2 marbles fro

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