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# 700 plus level question

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Manager
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700 plus level question [#permalink]  03 Aug 2011, 05:29
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
Please explain the steps to be followed?
Manager
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Re: 700 plus level question [#permalink]  03 Aug 2011, 05:45
In the group, there are 10 men & 5 women. So, a jury with atleast 2/3 men (~8 men) can be calculated as follows:

Desired jury could have either 8, 9 or 10 men and rest will be women accordingly.

We need to calculate: (10c8 * 5c4) + (10c9 * 5c3) + (10c10 * 5c2)

(10c8 * 5c4) is explained below:

4 women can be chosen in 5c4 ways = 5 ways
8 men can be chosen in 10c8 ways = 45 ways

Total ways to choose the desired jury of 12 = 5*45 = 225

similarly, we can solve rest and we will get 225+100+10 ways = 335 ways

Total ways to choose 12 from 15 is 15c12 = 455

Probability = 335/455 = 67/91.
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Re: 700 plus level question [#permalink]  04 Aug 2011, 02:05
Expert's post
ruturaj 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
Please explain the steps to be followed?

Another way to approach it:

Total jurors - 15
Men = 2/3 = 10
Women = 1/3 = 5

Jurors to be selected = 12
Men - atleast 2/3 = at least 8
Women - at most 1/3 = at most 4

The number of women selected can be 5 or less than 5. Less than 5 means at most 4. So if I find the probability of selecting 5 women and subtract it from 1, we will get the probability of selecting at most 4 women (the required probability)

Total number of ways of selecting the jurors = 15C12 = 15*14*13/3! = 455

Number of ways of selecting 5 women jurors (and 7 men) = 5C5 * 10C7 = 10*9*8/3! = 120

Probability of selecting 5 women jurors = 120/455 = 24/91
Probability of selecting at most 4 women jurors = 1 - 24/91 = 67/91
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Manager
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Re: 700 plus level question [#permalink]  04 Aug 2011, 07:47
@ Karishma, I liked your approach, it might save some precious time, thanks!
Manager
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Re: 700 plus level question [#permalink]  05 Aug 2011, 19:18
Approach is important if you want to solve the quant questions in time constraint !!!
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Re: 700 plus level question   [#permalink] 05 Aug 2011, 19:18
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