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Two teachers are randomly selected from a group of teachers

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Senior Manager
Senior Manager
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Joined: 10 Dec 2004
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Two teachers are randomly selected from a group of teachers [#permalink] New post 10 Jan 2005, 10:31
Two teachers are randomly selected from a group of teachers that includes 10 males and females, is the probability that both the two teachers are female more than 1/2?
(1) The number of female teachers is more than 5.
(2) The probability that both the two teachers are male is less than 1/10.

(1) is not Sufficient
(2) itself is not sufficient as well

OA is E. I just want to make know how to rule "C" out.
VP
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Joined: 18 Nov 2004
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 [#permalink] New post 10 Jan 2005, 11:07
Combine both the statements and assume x is number of male in the gp.

From statement 2:

xC2 / 10C2 = x(x-1) / 90 < 1/10 ===> x(x-1) < 9 .....(1)

From statement 1 female is > 5 so female can be 6, 7, 8, 9 or male can be 4, 3, 2, 1 in the gp

Testing eq 1 with statement 1...4 males doesn't satisfy eq 1. 3, 2 and 1 does.

So now u can have male, female combos (3, 7), (2,8), (1,9)

To get 2 females from each of the above cases p(e) = 9x8 / 90 = 0.8

56/90 = 0.62

42/90 = 0.46

As u see p(e) can be > than or < 0.5 ...thus insuff. So ans is E.


pb_india.....plz share the source of this ques...thx
Director
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Joined: 19 Nov 2004
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 [#permalink] New post 10 Jan 2005, 13:35
Kindly do not post the OA in the question or you can hide the OA is small white text. Posting the OA with the questions ruins the thrill of solving.

Thanks
nocilis
  [#permalink] 10 Jan 2005, 13:35
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Two teachers are randomly selected from a group of teachers

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