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# Lily has only red and blue balls in a jar. If she removes three balls,

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SC Moderator
Joined: 23 Sep 2015
Posts: 1382
Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

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10 Jun 2018, 06:21
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5
00:00

Difficulty:

95% (hard)

Question Stats:

30% (02:20) correct 70% (02:40) wrong based on 96 sessions

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Lily has only red and blue balls in a jar. If she removes three balls, is the probability of getting all red balls greater than the probability of getting at least one blue ball?

(1) The number of red balls is more than three times the number of blue balls.
(2) Less than (1)/(4) th of the balls in the jar are blue.

Source: Expert Global

_________________

Thanks!
Do give some kudos.

Simple strategy:
“Once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.”

Want to improve your Score:
GMAT Ninja YouTube! Series 1| GMAT Ninja YouTube! Series 2 | How to Improve GMAT Quant from Q49 to a Perfect Q51

My Notes:
Reading comprehension | Critical Reasoning | Absolute Phrases | Subjunctive Mood

Manager
Joined: 19 Feb 2017
Posts: 133
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

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10 Jun 2018, 07:50
Answer should be E. Eg: Take there are 4 red balls and 1 blue ball. Then P(RRR)= 2/5 and P(atleast 1B) = 3/5. So 2nd expression is smaller.

Then take there are 7 red balls and 1 blue ball. Then P(RRR)= 5/8 and P(atleast 1B) = 3/8. So 1st expression is smaller.

This example will work for both the statements. Therefore, no sufficiency in any. Hence, E.
Intern
Joined: 03 Sep 2015
Posts: 18
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

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28 Aug 2018, 09:13
Hi. How did you get 3/5 for blue balls?
Intern
Joined: 09 Aug 2018
Posts: 3
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

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29 Aug 2018, 04:37
1
Hi
I find the resource helpful, you can also try this probability lecture.
Intern
Joined: 03 Sep 2015
Posts: 18
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

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29 Aug 2018, 04:48
Thanks so much for this

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 480
Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

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29 Aug 2018, 05:57
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Quote:
Lily has only red and blue balls in a jar. If she gets three balls randomly, is the probability of getting all red balls greater than the probability of getting at least one blue ball?

(1) The number of red balls is more than three times the number of blue balls.
(2) Less than (1)/(4) of the balls in the jar are blue.

Source: Expert Global

Nice problem!

$$\operatorname{P} \left( {{\text{all}}\,\,3\,\,{\text{red}}} \right)\,\,\,\,\mathop > \limits^? \,\,\,\operatorname{P} \left( {{\text{not}}\,\,{\text{all}}\,\,3\,\,{\text{red}}} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\operatorname{P} \left( {{\text{all}}\,\,3\,\,{\text{red}}} \right) = \boxed{\frac{{C\left( {r,3} \right)}}{{C\left( {r + b,3} \right)}}\,\,\,\,\mathop > \limits^? \,\,\,\frac{1}{2}}$$

$$\left( {1 + 2} \right)\,\,$$

$$Take\,\,\left( {r,b} \right) = \left( {4,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{C\left( {4,3} \right)}}{{C\left( {5,3} \right)}} = \,\frac{1}{{10}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle$$

$$Take\,\,\left( {r,b} \right) = \left( {5,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{C\left( {5,3} \right)}}{{C\left( {6,3} \right)}} = \,\frac{{10}}{{20}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\,{\text{but}}\,\,\,{\text{increasing}}\,\,...$$

$$Take\,\,\left( {r,b} \right) = \left( {6,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{C\left( {6,3} \right)}}{{C\left( {7,3} \right)}} = \,\frac{4}{7}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,$$

(Keeping the number of blue balls fixed and increasing the number of red ones, we know the probability of getting 3 reds must increase...)

The answer is (E), because we were able to BIFURCATE (1+2)!

The above follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
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Lily has only red and blue balls in a jar. If she removes three balls, &nbs [#permalink] 29 Aug 2018, 05:57
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# Lily has only red and blue balls in a jar. If she removes three balls,

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