## Probability...

Math questions from mba.com and GMAT Prep software
saafiin
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### Probability...

Q: In a certain bag there are 12 identical blue balls, y identical yellow balls and no other ball. One ball will randomly removed. If the probability is less than 2/3 that the removed ball will be blue, then what is the least number of yellow balls that must be in the bag?

a. 17
b. 18
c. 19
d. 20
e. 21

RonPurewal
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### Re: Probability...

saafiin wrote:Q: In a certain bag there are 12 identical blue balls, y identical yellow balls and no other ball. One ball will randomly removed. If the probability is less than 2/3 that the removed ball will be blue, then what is the least number of balls that must be in the bag?

a. 17
b. 18
c. 19
d. 20
e. 21

i changed the text to something that makes sense with the given answer choices.

the problem wants the least number, so, try out the choices starting with the smallest one.

if there are (a) 17 balls -- 12 blue and 5 yellow -- then the probability of getting a blue one is 12/17, which is greater than 2/3. no good.

if there are (b) 18 balls -- 12 blue and 6 yellow -- then the probability of getting a blue one is 12/18, which is equal to 2/3. no good.

if there are (c) 19 balls -- 12 blue and 7 yellow -- then the probability of getting a blue one is 12/19, which is less than 2/3.

done. (c)
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krishnan.anju1987
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Posts: 125
Joined: Mon May 07, 2012 6:13 pm

### Re: Probability...

RonPurewal wrote:
saafiin wrote:Q: In a certain bag there are 12 identical blue balls, y identical yellow balls and no other ball. One ball will randomly removed. If the probability is less than 2/3 that the removed ball will be blue, then what is the least number of balls that must be in the bag?

a. 17
b. 18
c. 19
d. 20
e. 21

i changed the text to something that makes sense with the given answer choices.

the problem wants the least number, so, try out the choices starting with the smallest one.

if there are (a) 17 balls -- 12 blue and 5 yellow -- then the probability of getting a blue one is 12/17, which is greater than 2/3. no good.

if there are (b) 18 balls -- 12 blue and 6 yellow -- then the probability of getting a blue one is 12/18, which is equal to 2/3. no good.

if there are (c) 19 balls -- 12 blue and 7 yellow -- then the probability of getting a blue one is 12/19, which is less than 2/3.

done. (c)

Hi Ron,

A quick question. I found out algebraically that the least number of yellow balls were 7 but was then stumped when I saw double digit numbers as the answers for the yellow balls. Looks like either I misinterpreted the question and was expecting the answer to be the number of yellow balls instead of the total balls or the question is slightly wrong.
tim
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### Re: Probability...

yes the question is wrong. did you read Ron's post?
Tim Sanders
Manhattan GMAT Instructor

https://www.manhattanprep.com/gmat/forums/a-few-tips-t31405.html
krishnan.anju1987
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Posts: 125
Joined: Mon May 07, 2012 6:13 pm

### Re: Probability...

Guess I missed it. Thanks for confirming.
jnelson0612
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Joined: Fri Feb 05, 2010 10:57 am

### Re: Probability...

:-)
Jamie Nelson
ManhattanGMAT Instructor