Probability- Whats wrong with how my method??

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MBAsa: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Tue Apr 23, 2013 4:05 amFollowed by: 3 members; Thanked: 1 times

by MBAsa » Sat Jun 29, 2013 1:38 am

My answer to the following question was wrong. Can someone please explain whats wrong with my method.

Q:
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

A. 1/14 B.1/7 C.2/7 D. 3/7 E. 1/2

My solution:

To have exactly 2 women, there will also be 2 men, so my group will look like WWMM

Probablity of selecting W first = 5/8
Probablity of selecting W next = 4/7
Probablity of selecting M next= 3/6
Probablity of selecting M first = 2/5

Total probability = 5/8 * 4/7 * 3/6 * 2/5 = 1/14

I realize the order of picking does not matter. Even if it was MWMW, WMWM or MMWW my answer would be the same.

Answer = D[/list][/list]

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Source: Beat The GMAT — Problem Solving | Sat Jun 29, 2013 1:38 am

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 » Sat Jun 29, 2013 2:40 am

MBAsa wrote:My answer to the following question was wrong. Can someone please explain whats wrong with my method.

Q:
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

A. 1/14 B.1/7 C.2/7 D. 3/7 E. 1/2

My solution:

To have exactly 2 women, there will also be 2 men, so my group will look like WWMM

Probablity of selecting W first = 5/8
Probablity of selecting W next = 4/7
Probablity of selecting M next= 3/6
Probablity of selecting M first = 2/5

Total probability = 5/8 * 4/7 * 3/6 * 2/5 = 1/14

I realize the order of picking does not matter. Even if it was MWMW, WMWM or MMWW my answer would be the same.

Answer = D[/list][/list]

You have correctly determined the following:
P(WWMM) = 5/8 * 4/7 * 3/6 * 2/5 = 1/14.
This result represents the probability that the first and second people selected are women and that the third and fourth people selected are men.

But WWMM is only ONE WAY to select exactly two women.
To determine the total probability, we must account for ALL OF THE WAYS to select two women and one man.

Any arrangement of WWMM will yield exactly 2 W and 2 M.
Thus, the resulting probability above must be multiplied by the number of ways to arrange the 4 elements WWMM.
Number ways to arrange WWMM = 4!/(2!2!) = 6.
Thus:
P(exactly 2 women) = 1/14 * 6 = 3/7.

The correct answer is D.

I posted a complete solution for this problem in my two posts here:

https://www.beatthegmat.com/select-exact ... 88786.html

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Thu Jul 04, 2013 3:13 am

MBAsa wrote:My answer to the following question was wrong. Can someone please explain whats wrong with my method.

Q:
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

A. 1/14 B.1/7 C.2/7 D. 3/7 E. 1/2

My solution:

To have exactly 2 women, there will also be 2 men, so my group will look like WWMM

Probablity of selecting W first = 5/8
Probablity of selecting W next = 4/7
Probablity of selecting M next= 3/6
Probablity of selecting M first = 2/5

Total probability = 5/8 * 4/7 * 3/6 * 2/5 = 1/14

I realize the order of picking does not matter. Even if it was MWMW, WMWM or MMWW my answer would be the same.

Answer = D[/list][/list]

Select any 2 women = 5C2 = 10
Select any 2 men = 3C2 = 3
Favourable cases = 10 * 3 = 30

Sample space = (3+5)C4 = 70

Probability = 30/70 = 3/7

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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 Jul 04, 2013 11:15 pm

P of selecting excatly 2 women = 1 - P of selecting (1 women + 3 women + 4 women )

1 - ( 5/8*3/7*2/6*1/5*4 + 5/8*4/7*3/6*3/5*4 + 5/8*4/7*3/6*2/5)
1 - (1/14 + 3/7 + 1/14)
1 - 4/7 = 3/7

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