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If 2 different representatives are to be selected at random from a...

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If 2 different representatives are to be selected at random from a... [#permalink]

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New post 24 Jul 2016, 05:38
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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 1/2 of the 10 employees are women.
2. The probability that both representatives selected will be men is less than 1/10.

Please explain in detail your answer.
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Re: If 2 different representatives are to be selected at random from a... [#permalink]

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New post 24 Jul 2016, 06:04
EBITDA wrote:
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 1/2 of the 10 employees are women.
2. The probability that both representatives selected will be men is less than 1/10.

Please explain in detail your answer.


Answer should be E.

Statement 1: More than 1/2 of the 10 employees are women. Lets say 6 employee are women and 4 are men.

Probability of Both Women = 6c2/10c2 = 15/45=1/3 <1/2.

Now lets say 8 Women and 2 Men.

Probability of both Women = 8c2/10c2 = 28/45 > 1/2.

Hence, statement 1 is insufficient.

Statement 2 : The probability that both representatives selected will be men is less than 1/10.

Let say we have 3 Men and 7 Women.

probability of both men = 3c2/10c2= 3/45=1/15 < 1/10.

For this combination, we will have the probability of both women = 7c2/10c2=21/45 < 1/2

BUT, for 2 men and 8 Women, probability of both men = 1/45 <1/10

and we have calculated above that probability of both Women in this case > 1/2.

Hence, Insufficient.

Combining the statements also doesn't provide any solution. Hence, answer is E
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Re: If 2 different representatives are to be selected at random from a... [#permalink]

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New post 24 Jul 2016, 07:58
EBITDA wrote:
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 1/2 of the 10 employees are women.
2. The probability that both representatives selected will be men is less than 1/10.

Please explain in detail your answer.


Discussed here: if-2-different-representatives-are-to-be-selected-at-random-128233.html

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Re: If 2 different representatives are to be selected at random from a... [#permalink]

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Re: If 2 different representatives are to be selected at random from a...   [#permalink] 12 Sep 2017, 15:33
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