A committee of 2 people is to be formed from a group of 8

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A committee of 2 people is to be formed from a group of 8 [#permalink]

22 Jan 2011, 03:06

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A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?

(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

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Re: A committee of 2 people, is P > 0.25? [#permalink]

22 Jan 2011, 03:32

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MichelleSavina wrote:

Q) A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?
(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

Given: m+w=8. Question: is \frac{m}{8}*\frac{m-1}{7}>\frac{1}{4}? --> is m(m-1)>14 --> is m\geq{5}? So the question basically asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7).

(1) More than 40% of the employees are men --> m>0.4*8 --> m>3.2: there may be 4 men and in this case the answer to the question will be NO or there may be more than 4 men (5, 6, ...) and in this case the answer to the question will be YES. Not sufficient.

(2) The probability that both the selected people will be women is more than 20% -> \frac{w}{8}*\frac{w-1}{7}>\frac{1}{5} --> w(w-1)>11.2 --> is w\geq{4}: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

Answer: B.
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Re: A committee of 2 people is to be formed [#permalink]

19 May 2012, 09:39

gmihir wrote:

A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men.If P is the probability that both the selected people are men, is P > 0.25?
(1) More than 40% of the employees are men.
(2) The probability that both the selected people will be women is more than 20%.

This is my first answer here... so I dont know how to use maths symbols here...

Probability that both men are selected is MC2/8C2. We have to find whether this is greater than 1/4.
If you solve : MC2/8C2 > 1/4, it gives you M^2 - M - 14 >0 which is true for M > 4.

So the first option is ruled out because 40% of 8 is 3.2, which means M can either 4 or greater than 4.

2. If you solve the second option, WC2/8C2 > 1/2, it gives W^2 - W- 11 > 0, which is true for W >= 4. Since total people are 8, M <= 4.

So, the answer is B.

Hope its clear.

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Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

20 May 2012, 10:48

(2) The probability that both the selected people will be women is more than 20% -> \frac{w}{8}*\frac{w-1}{7}>\frac{1}{5} --> w(w-1)>11.2 --> is w\geq{4}: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

can you explain what this equaiton means? W(W-1) >11.2 How do we know its SUFF by this equation?

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Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

20 May 2012, 11:27

gmihir wrote:

Merging similar topics. Please refer to the solution above.

dchow23 wrote:

The question asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7). From (2) we have that w(w-1)>11.2. Now, if the # of women is 3 then 3(3-1)=6<11.2, so w>3, which means that there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 8-4=4, 8-5=3, ... So, the answer to the question whether there are more than or equal to 5 men is NO.

Hope it's clear.
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Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

15 Jun 2012, 03:07

Good question and great explanation... thanks
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Re: A committee of 2 people is to be formed from a group of 8 [#permalink] 15 Jun 2012, 03:07

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A committee of 2 people is to be formed from a group of 8

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