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# Two players are to be selected from a football team which consists of

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Senior Manager
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 423

Kudos [?]: 157 [1], given: 422

Location: India
GPA: 3.64
Two players are to be selected from a football team which consists of [#permalink]

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29 Oct 2017, 09:12
1
KUDOS
00:00

Difficulty:

75% (hard)

Question Stats:

34% (00:51) correct 66% (01:30) wrong based on 32 sessions

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Two players are to be selected from a football team which consists of 10 football players. Is the probability that both the players chosen will be left backs greater than 50 %?

(1) The probability that both players selected will not be left backs is less than 10 %
(2) More than fifty percent of the players are left backs.

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[Reveal] Spoiler: OA

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When the going gets tough, the tough gets going...

Kudos [?]: 157 [1], given: 422

Math Expert
Joined: 02 Aug 2009
Posts: 5522

Kudos [?]: 6418 [0], given: 122

Re: Two players are to be selected from a football team which consists of [#permalink]

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29 Oct 2017, 19:09
souvonik2k wrote:
Two players are to be selected from a football team which consists of 10 football players. Is the probability that both the players chosen will be left backs greater than 50 %?

(1) The probability that both players selected will not be left backs is less than 10 %
(2) More than fifty percent of the players are left backs.

Please give kudos, if u liked my post!

Hi...

A good Q..

So we have to choose 2 out of 10.
(1) The probability that both players selected will not be left backs is less than 10 %
Let there be x non left backs, so prob of choosing both is $$\frac{x}{10}*\frac{x-1}{10}<\frac{10}{100}$$...
So x(x-1)<10....
x =3 or <3 because 4*3=12>10 and 3*2=6<10...
So if x=3, left backs are 10-3=7
Prob =7/10*6/9=42/90<50%
If x=2, prob =8/10*7/9=56/90>50%
So insuff

(2) More than fifty percent of the players are left backs.
Say there are 6 or 7, as seen above itwill be <50%
And above 8,9 or 10, prob will be >50%
Insufficient

Combined..
If it is 7, Ans is NO
If 8,9 or 10, Ans is YES
Insufficient

E
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Kudos [?]: 6418 [0], given: 122

Re: Two players are to be selected from a football team which consists of   [#permalink] 29 Oct 2017, 19:09
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