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Please help!! Tricky probability question

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by dddanny2006 » Thu Nov 21, 2013 3:09 pm
In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is female?

A)1/20
B)1/10
C)1/5
D)2/5
E)3/4

ANSWER-B Source-Magoosh

I did it this way- P(Advanced degree) AND P(Female)
(100/400)*(100/400) =1/16

I have not been able to apply the Manhattan Concepts in this problem.Im finding probability difficult,please advice on going about it.

Thanks
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by Brent@GMATPrepNow » Thu Nov 21, 2013 3:47 pm
dddanny2006 wrote:In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is female?

A)1/20
B)1/10
C)1/5
D)2/5
E)3/4
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

P(event A occurs) = (# of ways for event A to occur)/(total # of outcomes)
So, P(selected employee is female with advanced degree) = (# of females with advanced degrees)/(total number of employees)

There are 400 employees. In other words, there are 400 possible outcomes.

We're told that there are 100 females, and that 40% of them have advanced degrees.
40% of 100 = 40, so there are 40 females that have advanced degrees.

So, P(selected employee is female with advanced degree) = (40)/(400)
= [spoiler]1/10[/spoiler]
= B

Cheers,
Brent
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by dddanny2006 » Thu Nov 21, 2013 3:50 pm
Oh ok.I did not know this method.Ive been studying from Manhattan.Where can I learn such techniques?Also,why was my strategy wrong?
Brent@GMATPrepNow wrote:
dddanny2006 wrote:In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is female?

A)1/20
B)1/10
C)1/5
D)2/5
E)3/4
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

P(event A occurs) = (# of ways for event A to occur)/(total # of outcomes)
So, P(selected employee is female with advanced degree) = (# of females with advanced degrees)/(total number of employees)

There are 400 employees. In other words, there are 400 possible outcomes.

We're told that there are 100 females, and that 40% of them have advanced degrees.
40% of 100 = 40, so there are 40 females that have advanced degrees.

So, P(selected employee is female with advanced degree) = (40)/(400)
= [spoiler]1/10[/spoiler]
= B

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Nov 21, 2013 3:59 pm
dddanny2006 wrote:In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is female?

A)1/20
B)1/10
C)1/5
D)2/5
E)3/4

ANSWER-B Source-Magoosh

I did it this way- P(Advanced degree) AND P(Female)
(100/400)*(100/400) =1/16

I have not been able to apply the Manhattan Concepts in this problem.Im finding probability difficult,please advice on going about it.

Thanks
Your approach is fine.
However, we need to recognize that the two probabilities are not independent.
We need to use the formula P(A and B) = P(A) x P(B|A)
So, P(advanced degree AND female) = P(advanced degree) x P(female|advanced degree)

P(female|advanced degree) = probability that selected person is female GIVEN THAT the selected person has an advanced degree.

So, there are 100 people with an advanced degree and OF THOSE 100 people, 40 are female.
So, P(female|advanced degree) = 40/100

Now let's put it all together.

P(advanced degree AND female) = P(advanced degree) x P(female|advanced degree)
= (100/400) x (40/100)
= [spoiler]1/10[/spoiler]
= B

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Nov 21, 2013 4:01 pm
dddanny2006 wrote:Where can I learn such techniques?
I'm assuming that most (actually all) of the test prep companies on this site (including ours :-)) cover this technique.

Cheers,
Brent
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by dddanny2006 » Thu Nov 21, 2013 4:04 pm
Manhattan has a very small section in the Number Properties book with just AND and OR concepts.Theres nothing such as Independent,dependent,disjoint etc. in there.
Brent@GMATPrepNow wrote:
dddanny2006 wrote:Where can I learn such techniques?
I'm assuming that most (actually all) of the test prep companies on this site (including ours :-)) cover this technique.

Cheers,
Brent
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by theCodeToGMAT » Thu Nov 21, 2013 10:39 pm
400 = 300(males) + 100(females)

20% of 300 = Advanced degree
40% of 100 = Advanced degree

PRobability = Female employee with advanced degree

==> (40% of 100)/(400)

==> 40/400

==> 1/10
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by theCodeToGMAT » Thu Nov 21, 2013 10:49 pm
dddanny2006 wrote:
I did it this way- P(Advanced degree) AND P(Female)
(100/400)*(100/400) =1/16

I have not been able to apply the Manhattan Concepts in this problem.Im finding probability difficult,please advice on going about it.

Thanks
dddanny2006, you need to completely understand the question before moving forward with the soltion. If you are confident on one method, then you can solve mostly all the questions..

We know that 40% of 100 Females have advanced studies.. So, the total count is "40" ==> 40/400
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