Another probability question..making mistakes!

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dddanny2006: Master | Next Rank: 500 Posts; Posts: 209; Joined: Thu Jan 12, 2012 12:59 pm

by dddanny2006 » 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

ANSWER-D Source-Magoosh

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

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Source: Beat The GMAT — Problem Solving | Thu Nov 21, 2013 3:10 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » 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.

The correct answer is D.

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » 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

ANSWER-D Source-Magoosh

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

Hence Answer is D

Hope it helps you.

Regards,
Uva.

Known is a drop Unknown is an Ocean

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Thu Nov 21, 2013 8:21 pm

P(Ad digree or female) = P(Ad digree) + P (female) - P(Ad digree and female)
= 1/4 + 1/4 - 1/10 = 2/5

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riz_gmat: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Thu Sep 26, 2013 9:05 pm; Thanked: 5 times

by riz_gmat » 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 ?

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » 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.

So, it is enough to add the probability of Male with Advanced degree. We no need to add again the Female with advanced degree, since it has already been added.

Hope it helps you.

Regards,
Uva.

Known is a drop Unknown is an Ocean

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » 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

We see that 100 total employees had an advanced degree.

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) = P(female) + P(advanced degree) - P(both)

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

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

Answer: D

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Head of GMAT Instruction
[email protected]

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