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Another probability question..making mistakes!

This topic has 2 expert replies and 4 member replies
dddanny2006 Master | Next Rank: 500 Posts
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Another probability question..making mistakes!

Thu Nov 21, 2013 3:10 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 or is female?

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

I did it this way- P(Advanced degree) OR P(Female)
(100/400)+(100/400) =1/2

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

Thanks

GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Thu Nov 21, 2013 5:58 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 or is female?

A)1/20
B)1/10
C)1/5
D)2/5
E)3/4
P = (good outcomes)/(all possible outcomes).

Here, it might be easier to count each part of the fraction separately.

All:
There are 400 employees.
Thus, the total number of possible outcomes = 400.

Good outcomes:
Of these 400 employees, any employee who is female or who has an advanced degree will constitute a good outcome.
Females = 100.
Since 20% of the men have advanced degrees, males with advanced degrees = .2(300) = 60.
Thus:
The total number of good outcomes = 100+60 = 160.

Resulting probability:
good/all = 160/400 = 16/40 = 2/5.

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Uva@90 Master | Next Rank: 500 Posts
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Thu Nov 21, 2013 7:32 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 or is female?

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

I did it this way- P(Advanced degree) OR P(Female)
(100/400)+(100/400) =1/2

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 have added the female employee who has additional degree i.e. 40 twice.

P(Female) = 100/400
P(Advanced degree other than female) = 60/400

100/400 + 60/400 = 2/5

Hope it helps you.

Regards,
Uva.

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Known is a drop Unknown is an Ocean

vipulgoyal Master | Next Rank: 500 Posts
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Thu Nov 21, 2013 8:21 pm
= 1/4 + 1/4 - 1/10 = 2/5

riz_gmat Junior | Next Rank: 30 Posts
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Thu Nov 21, 2013 8:37 pm
Hi GMATGuruNY

But Question here is what is the probability this employee has an advanced degree or is female?

ie, Probability of that employee having advanced degree or Probability of that employee being female.
Nowhere in the question, it is mentioned employee having advanced degree cannot be female! Then why do you consider probability of male employees alone with advanced degree ?

Uva@90 Master | Next Rank: 500 Posts
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Thu Nov 21, 2013 10:02 pm
riz_gmat wrote:
Hi GMATGuruNY

But Question here is what is the probability this employee has an advanced degree or is female?

ie, Probability of that employee having advanced degree or Probability of that employee being female.
Nowhere in the question, it is mentioned employee having advanced degree cannot be female! Then why do you consider probability of male employees alone with advanced degree ?
Hi Riz_gmat,
What you said is partially right.
what question stated is "probability this employee has an advanced degree or is female?"
what Mitch did is,
First he calculated the probability of Female
then he calculated the probability of Male with Advanced degree.
probability of Female it includes both Female with Advanced degree and without advanced degree.

Hope it helps you.

Regards,
Uva.

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Known is a drop Unknown is an Ocean

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Jeff@TargetTestPrep GMAT Instructor
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Thu Dec 07, 2017 6:31 am
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 or is female?

A)1/20
B)1/10
C)1/5
D)2/5
E)3/4
We are given that there are 400 total employees - 100 female and 300 male. We are also given that 20% of the male employees have advanced degree and that 40% of the females have advanced degrees.

Thus,

0.2 x 300 = 60 males with advanced degrees

And

0.4 x 100 = 40 females with advanced degrees

Since there are females with advanced degrees we have to subtract out any overlap when determining the probability of selecting a female or an employee with an advanced degree.

P(female or advanced degree) = 100/400 + 100/400 - 40/400

P(female or advanced degree) = 160/400 = 16/40 = 2/5

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Jeffrey Miller Head of GMAT Instruction

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