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# Two teachers are randomly selected from a group of teachers

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Senior Manager
Joined: 10 Dec 2004
Posts: 274
Followers: 1

Kudos [?]: 52 [0], given: 0

Two teachers are randomly selected from a group of teachers [#permalink]  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
Joined: 18 Nov 2004
Posts: 1442
Followers: 2

Kudos [?]: 20 [0], given: 0

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
Joined: 19 Nov 2004
Posts: 563
Location: SF Bay Area, USA
Followers: 3

Kudos [?]: 57 [0], given: 0

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
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