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# If 2 different representatives are to be selected at random

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Senior Manager
Joined: 14 Jul 2006
Posts: 281
If 2 different representatives are to be selected at random [#permalink]

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23 Aug 2006, 00:09
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If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2 ?
(1) More than 5 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10 .
CEO
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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23 Aug 2006, 00:20
E

Let w = women
m = men

St1: least prob is 6/10 * 5/9 = 1/3 and max prob is 1.: INSUFF

St2: m/10 * (m-1)/9 < 1/10
i.e m * (m-1) < 9
i.e m are either 0,1,2 or 3.
So women are greater than 6.
least prob is 7/10 * 6/9 = 1/15 max prob is 1: INSUFF

Together:
We get women are greater than 6. Same as statement 2.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
Joined: 14 Jul 2006
Posts: 281

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23 Aug 2006, 00:25
yup as usual your right on the money
Manager
Joined: 09 Jul 2006
Posts: 85
Location: India

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23 Aug 2006, 09:11
ps_dahiya wrote:
E

St1: least prob is 6/10 * 5/9 = 1/3 and max prob is 1.: INSUFF

in this particular step, I always get confused.
I dont know what rule to apply to get probability of selecting 2 women.
Choice 1:
Like you have done probablility = 6/10 * 5/9
Choice 2: (what I did when trying to solve this problem on my own!)
Least Probability = 1/6*1/5
(out of 6 women, probability of selecting the first is 1/6. now that one is selected, the probability of selecting the next is 1 out of the 5 remaining).

what i would like to know is why you have taken choice 1 and not choice 2. is there a particular formula / method that indicates when to use what pls ?
any help on this would be highly appreciated.
thanks.
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Prashrash.

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Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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23 Aug 2006, 15:08
prashrash wrote:
ps_dahiya wrote:
E

St1: least prob is 6/10 * 5/9 = 1/3 and max prob is 1.: INSUFF

in this particular step, I always get confused.
I dont know what rule to apply to get probability of selecting 2 women.
Choice 1:
Like you have done probablility = 6/10 * 5/9
Choice 2: (what I did when trying to solve this problem on my own!)
Least Probability = 1/6*1/5
(out of 6 women, probability of selecting the first is 1/6. now that one is selected, the probability of selecting the next is 1 out of the 5 remaining).

what i would like to know is why you have taken choice 1 and not choice 2. is there a particular formula / method that indicates when to use what pls ?
any help on this would be highly appreciated.
thanks.

Choice 2 is wrong.

I simply ask: What is the prob of selecting a women from a group of 6 women and 4 men. It will be 6/10.
Now we have selected a women there are 5 women remaining and total of 9 people remaining. Prob of selecting a women from a group of 5 women and 4 men. It is 5/9
So prob that first one is women and second one is also women = 6/10 * 5/9

Hope this helps.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
Joined: 15 Aug 2004
Posts: 327

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24 Aug 2006, 06:32
prashrash wrote:
Choice 2: (what I did when trying to solve this problem on my own!)
Least Probability = 1/6*1/5
(out of 6 women, probability of selecting the first is 1/6. now that one is selected, the probability of selecting the next is 1 out of the 5 remaining).

Choice 2 come sinto play when you want to select a particular woman from that group.... Lest say you had to choose Jenny and Katie both... then you can used Choice 2...
Manager
Joined: 09 Jul 2006
Posts: 85
Location: India

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24 Aug 2006, 09:13
Thanks guys. Appreciate the explanations. Yes, they have helped me to a great extent.
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Cheers!
Prashrash.

Senior Manager
Joined: 15 Aug 2004
Posts: 327

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25 Aug 2006, 01:02
ps_dahiya wrote:
sumitsarkar82 wrote:
prashrash wrote:
Choice 2: (what I did when trying to solve this problem on my own!)
Least Probability = 1/6*1/5
(out of 6 women, probability of selecting the first is 1/6. now that one is selected, the probability of selecting the next is 1 out of the 5 remaining).

Choice 2 come sinto play when you want to select a particular woman from that group.... Lest say you had to choose Jenny and Katie both... then you can use Choice 2...

That is so correct.

Learnt it from you sir
25 Aug 2006, 01:02
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# If 2 different representatives are to be selected at random

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