Problem Solving

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.

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?

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

That makes much more sense and a better approach than my way.

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?

I felt I got lucky with the approach. Thanks for explaining it depth.

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!

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