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

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

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New post 29 Oct 2017, 10:12
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Question Stats:

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

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New post 29 Oct 2017, 20:09
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.

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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

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Two players are to be selected from a football team which consists of &nbs [#permalink] 29 Oct 2017, 20:09
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