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If the probability of choosing 2 red marbles without replac [#permalink]
Expert's post 00:00

Question Stats: 68% (01:44) correct 31% (04:22) wrong based on 61 sessions

If the probability of choosing 2 red marbles without replacement from a bag of only red and blue marbles is $$\frac{3}{55}$$ and there are 3 red marbles in the bag, what is the total number of marbles in the bag?

A) 10

B) 11

C) 55

D) 110

E) 165
[Reveal] Spoiler: OA

_________________ GRE Instructor Joined: 10 Apr 2015
Posts: 1962
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Re: If the probability of choosing 2 red marbles without replac [#permalink]
1
KUDOS
Expert's post
Carcass wrote:

If the probability of choosing 2 red marbles without replacement from a bag of only red and blue marbles is $$\frac{3}{55}$$ and there are 3 red marbles in the bag, what is the total number of marbles in the bag?

A) 10
B) 11
C) 55
D) 110
E) 165

Let T = the TOTAL number of marbles in the bag.
We are told that 3 of those marbles are red

P(select a red marble first) = 3/T
Once we've removed the first red marble, there are T-1 marbles remaining and 2 of them are red
So, P(select a red marble second) = 2/(T-1)

Okay, now let's use probability rules to answer the question....

P(select 2 red marbles) = P(select a red marble first AND select a red marble second)
= P(select a red marble first) x P(select a red marble second)
= 3/T x 2/(T-1)
= 6/(T² - T)

We're told that P(select 2 red marbles) = 3/55
So, we can write: 6/(T² - T) = 3/55
Cross multiply to get: 3(T² - T) = (6)(55)
Divide both sides by 3 to get: T² - T = (2)(55)
Evaluate: T² - T = 110
Rearrange: T² - T - 110 = 0
Factor: (T - 11)(T + 10) = 0

So, EITHER T = 11 OR T = -10
Since T cannot be negative, it must be the case that T = 11

[Reveal] Spoiler:
B

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Intern Joined: 22 Dec 2017
Posts: 2
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Re: If the probability of choosing 2 red marbles without replac [#permalink]
1
KUDOS
An easy approach :
Let no: of blue bags be B. Given no: of red bags is 3. Thus
3/(3+B) * 2/(3+B-1) = 3/55 (Probablity without replacement formula)
We need to know 3+B
On solving,
(3+B)(3+B-1)=110
Thus 3+B is 11
Intern Joined: 22 Apr 2016
Posts: 35
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Kudos [?]: 0 , given: 2

If the probability of choosing 2 red marbles without replacement from a bag of only red and blue marbles is and there are 3 red marbles in the bag, what is the total number of marbles in the bag?355
A 10

B 11

C 55

D 110

E 165 Word Problem   [#permalink] 26 Mar 2019, 00:19
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