|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 13 Jan 2008
Posts: 24
Followers: 0
Kudos [?]:
7
[1] , given: 0
|
If a jury of 12 people is to be selected randomly from a [#permalink]
 04 Feb 2008, 16:40
1
This post received
KUDOS
Question Stats:
28% (02:28) correct
71% (02:03) wrong based on 7 sessions
If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
24/91
45/91
2/3
67/91
84/91
|
|
|
|
|
|
|
Director
Joined: 12 Jul 2007
Posts: 875
Followers: 8
Kudos [?]:
137
[4] , given: 0
|
Re: potential jury members [#permalink]
04 Feb 2008, 17:32
4
This post received
KUDOS
We have a pool of 10 men and 5 women
We need a jury of 12 people
What is the probability that the jury will comprise at least 2/3 men?
2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.
15C12 = 455 ways to select a jury of 12 from a pool of 15
5C5 = 1 way to select all 5 women
10C7 = 120 ways to select 7 men from a pool of 10
1*120 = 120 ways to select a jury with fewer than 8 men
(455-120)/455 = 335/455 = 67/91
Answer D
|
|
|
|
|
|
Senior Manager
Joined: 20 Dec 2004
Posts: 268
Followers: 6
Kudos [?]:
44
[0], given: 0
|
Re: potential jury members [#permalink]
04 Feb 2008, 18:37
+1 for the question and +1 for the excellent approach....
_________________
Stay Hungry, Stay Foolish
|
|
|
|
|
|
Intern
Joined: 13 Jan 2008
Posts: 24
Followers: 0
Kudos [?]:
7
[0], given: 0
|
Re: potential jury members [#permalink]
06 Feb 2008, 15:35
eschn3am wrote: We have a pool of 10 men and 5 women
We need a jury of 12 people
What is the probability that the jury will comprise at least 2/3 men?
2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.
15C12 = 455 ways to select a jury of 12 from a pool of 15
5C5 = 1 way to select all 5 women
10C7 = 120 ways to select 7 men from a pool of 10
1*120 = 120 ways to select a jury with fewer than 8 men
(455-120)/455 = 335/455 = 67/91
Answer D clear answer, thanks - one question though, the numerator is 455-120; is that 120 because you have multiplied by the 1? i.e. if there were two ways, would it have been 120*2 leading to 455-240?
|
|
|
|
|
|
Director
Joined: 01 May 2007
Posts: 809
Followers: 1
Kudos [?]:
37
[0], given: 0
|
Re: potential jury members [#permalink]
06 Feb 2008, 16:07
Can you show how to solve this using probabilities?
|
|
|
|
|
|
SVP
Joined: 28 Dec 2005
Posts: 1612
Followers: 1
Kudos [?]:
54
[0], given: 2
|
Re: potential jury members [#permalink]
06 Feb 2008, 16:34
i did this the long way ... got the right answer, but should have timed myself. oh, and then i banged my head on the wall after seeing the clever approach taken by our resident math expert above !
we want at least 8 men on the jury. so 8 m, 4w, or 9m, 3w or 10m and 2 w.
i calculated the # ways of each case individually: 8m and 4w is given by (10C8)*(5C4). Follow that approach for the others..
Overall outcomes is 15C12 = 455
You end up with 335/455
|
|
|
|
|
|
Director
Joined: 01 May 2007
Posts: 809
Followers: 1
Kudos [?]:
37
[0], given: 0
|
Re: potential jury members [#permalink]
06 Feb 2008, 16:46
Anytime a problem ask for a "atleast" there is a good chance you can use the "1-Something" trick IMHO.
|
|
|
|
|
|
Director
Joined: 12 Jul 2007
Posts: 875
Followers: 8
Kudos [?]:
137
[0], given: 0
|
Re: potential jury members [#permalink]
06 Feb 2008, 18:54
gmatraider wrote: eschn3am wrote: We have a pool of 10 men and 5 women
We need a jury of 12 people
What is the probability that the jury will comprise at least 2/3 men?
2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.
15C12 = 455 ways to select a jury of 12 from a pool of 15
5C5 = 1 way to select all 5 women
10C7 = 120 ways to select 7 men from a pool of 10
1*120 = 120 ways to select a jury with fewer than 8 men
(455-120)/455 = 335/455 = 67/91
Answer D clear answer, thanks - one question though, the numerator is 455-120; is that 120 because you have multiplied by the 1? i.e. if there were two ways, would it have been 120*2 leading to 455-240? The 120 is the number of possibilities where there are FEWER than 2/3 men on the jury. 455 is the number of possible ways to make up this jury. If there are 455 ways total, and 120 of those ways have fewer than 2/3 men...then (455-120) is the number of possible ways where the jury IS at least 2/3 men. We're looking for the probability that the jury will be at least 2/3 men so (455-120)/455 is our equation.
|
|
|
|
|
|
CEO
Joined: 29 Mar 2007
Posts: 2618
Followers: 13
Kudos [?]:
144
[0], given: 0
|
Re: potential jury members [#permalink]
06 Feb 2008, 23:45
gmatraider wrote: If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
24/91
45/91
2/3
67/91
84/91 This prob took me a sweet 5minutes =(. We have 15!/12!3! ways of arranging them w/ no constraints = 455 Now we have 10!/8!2! ways for 8 men --> 45 10!/9! ways for 9 men --> 10 10!/10! ways for 10men --> 1 Now for women: 5!/4! for 4 women --> 5 5!/2!3! for 3 women --> 10 5!/3!2! for 2 women --> 10 Now its just 45*5=225 10*10=100 10*1=10 335/455 --> 67/91 D
|
|
|
|
|
|
Forum Moderator
Status: doing good things...
Joined: 02 Jul 2009
Posts: 1234
Concentration: Entrepreneurship, Finance
GMAT 1: Q V
GMAT 2: 690 Q49 V35
GPA: 3.77
WE: Corporate Finance (Other)
Followers: 126
Kudos [?]:
419
[1] , given: 523
|
Re: potential jury members [#permalink]
09 Aug 2010, 13:03
1
This post received
KUDOS
It is very easy . I have solved this in less than a minute without combinatorics.  there are total 10 men and 5 women in 12 jury members, could be: M W T 10+2=12 9+3=12 8+4=12 7+5=12 M-men , W-women T - total So out of 4 possible outcomes 3 are favorbale, 1 is unfavorable, favorbale is 3/4=0.75 67/91~73%., which is the closest to 3/4. Bingo! 
_________________
Follow me, if you find my explanations useful.
Audaces fortuna juvat!
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 08 Oct 2010
Posts: 215
Location: Uzbekistan
Schools: Johnson, Fuqua, Simon, Mendoza
WE 3: 10
Followers: 7
Kudos [?]:
104
[0], given: 974
|
Re: potential jury members [#permalink]
13 Jan 2011, 09:18
In is difficult to understand the question stem because of incorrect grammatical construction. The right to introduce this question must such “If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jurors’ pool consists of 2/3 men and 1/3 women, what is the probability that at least 2/3 of the jury will comprise of men?”
If the question stem were in the construction I have formulated above everybody would catch the point better. Frankly speaking it was difficult for me to recognize the pattern and to comprehend conditions of this question. I would request gmatraider to be more precise and orderly in representation of his/her questions.
|
|
|
|
|
|
|
Re: potential jury members
[#permalink]
13 Jan 2011, 09:18
|
|
|
|
|
|
|
|
|
|
|
close
