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English teachers - Probability

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by crackgmat007 » Fri Aug 07, 2009 2:05 pm
The membership of a committee consists of 3 English teachers, 4
Mathematics teachers, and 2 Social Studies teachers. If 2
committee members are to be selected at random to write the
committee’s report, what is the probability that the two members
selected will both be English teachers?
A. 2/3
B. 1/3
C. 2/9
D. 1/12
E. 1/24

OA - D Pls explain.
Last edited by crackgmat007 on Sat Aug 08, 2009 3:49 pm, edited 1 time in total.
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by georgeung » Fri Aug 07, 2009 2:57 pm
I'm curious to know if this is simple probability formula:

probability = (Desired Outcomes) / (Possible Outcomes)

3 x 4 x 2 = 24
desired outcomes = 2

2/24 = 1/12.

Is this solution more complicated than I think it is?
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by jsk988 » Sat Aug 08, 2009 6:19 am
I'm not sure if the above is the correct approach even though you get the same answer.

the probability that you select an english teacher on the first pick is 3/9 and the the second pick is 2/8...

this gives you 1/3 * 1/4 = 1/12
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by georgeung » Sat Aug 08, 2009 7:06 am
That makes much more sense and a better approach than my way.
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by ankitns » Sat Aug 08, 2009 9:43 am
I think you just got lucky with this approach...:)
I would not use it on the test...

how do you have the desired outcomes of 2? If we have 3 teachers, (A, B, C) we could have AB, AC and BC. Giving us 3 desired outcomes...

Secondly, the total possible outcomes is not 3*4*2 but 9choose2 = 9!/(2!*7!) giving us 9 * 4

Since probability = (Desired Outcomes) / (Possible Outcomes)
= 3 / (9 * 4)
= 1 / (3 * 4)
= 1 / 12


Alternatively, you could also use the approach taken by jsk988...even that is correct...

Cheers.
georgeung wrote:I'm curious to know if this is simple probability formula:

probability = (Desired Outcomes) / (Possible Outcomes)

3 x 4 x 2 = 24
desired outcomes = 2

2/24 = 1/12.

Is this solution more complicated than I think it is?
Attempt 1: 710, 92% (Q 42, 63%; V 44, 97%)
Attempt 2: Coming soon!
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by georgeung » Sat Aug 08, 2009 10:56 am
I felt I got lucky with the approach. Thanks for explaining it depth.
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Re: English teachers - Probability

by shahdevine » Sat Aug 08, 2009 11:10 am
crackgmat007 wrote:The membership of a committee consists of 3 English teachers, 4
Mathematics teachers, and 2 Social Studies teachers. If 2
committee members are to be selected at random to write the
committee’s report, what is the probability that the two members
selected will both be English teachers?
A. 2/3
B. 1/3
C. 2/9
D. 1/12
E. 1/24

OA - D Pls explain.
this is pretty straight forward probability problem.

p(English) and p(english)=3/9*2/8=6/72=1/12

you got this man!
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Re: English teachers - Probability

by quant-master » Sat Aug 08, 2009 11:11 am
crackgmat007 wrote:The membership of a committee consists of 3 English teachers, 4
Mathematics teachers, and 2 Social Studies teachers. If 2
committee members are to be selected at random to write the
committee’s report, what is the probability that the two members
selected will both be English teachers?
A. 2/3
B. 1/3
C. 2/9
D. 1/12
E. 1/24

OA - D Pls explain.
its 3c2/9c2 = 3/36 = 1/12

hence D

Thanks,
Quant-Master
https://gmat-quants.blocked - My Blog Updated almost daily with new quant fundas. Find collection of quants question in my blog
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