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There are 50 balls. 20 are red, 20 are green, 6 are blue, 4

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VP
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There are 50 balls. 20 are red, 20 are green, 6 are blue, 4 [#permalink] New post 30 Aug 2007, 17:24
There are 50 balls. 20 are red, 20 are green, 6 are blue, 4 are black. What is the probability of drawing two balls of the same color?
Senior Manager
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 [#permalink] New post 30 Aug 2007, 18:53
20/50*19/49 + 20/50*19/49 +6/50*5/49 +4/50*3/49
=401/1225

The number is kind of weird. But it should be this concept.
GMAT Club Legend
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 [#permalink] New post 30 Aug 2007, 18:57
Winning cases: 2 red, 2 green, 2 blue or 2 black

P(Red) and P(Red) = 20/50 * 19/49 = 35/245
P(Green) and P(Green) = 20/50 * 19/49 = 35/245
P(Blue) and P(Blue) = 6/50 * 5/49 = 3/245
P(Black) and P(Black) = 4/50 * 3/49 = 6/1225

Total = 53/175
Director
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Re: Probability [#permalink] New post 30 Aug 2007, 19:50
bkk145 wrote:
There are 50 balls. 20 are red, 20 are green, 6 are blue, 4 are black. What is the probability of drawing two balls of the same color?


Agreed with above,

we can also use combination method, should yeild the same result

(2C20+2C20+2C6+2C4)/ 2C50

of course, for these numbers better use method above.
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Re: Probability [#permalink] New post 30 Aug 2007, 20:04
bkk145 wrote:
There are 50 balls. 20 are red, 20 are green, 6 are blue, 4 are black. What is the probability of drawing two balls of the same color?


You have to calculate all scenarios and then add them together.

Red: 20/50*19/49= 380/2450

Green: 20/50*19/49=380/2450

Blue: 6/50*5/49= 30/2450

Black: 4/50*3/49= 12/2450

Add all the fractions up

801/2450 or 401/1225
Director
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Re: Probability [#permalink] New post 30 Aug 2007, 20:31
IrinaOK wrote:
bkk145 wrote:
There are 50 balls. 20 are red, 20 are green, 6 are blue, 4 are black. What is the probability of drawing two balls of the same color?


Agreed with above,

we can also use combination method, should yeild the same result

(2C20+2C20+2C6+2C4)/ 2C50

of course, for these numbers better use method above.


i take this one:

p = (20C2 + 20C2 + 6C2 + 4C2) / 2C50
VP
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 [#permalink] New post 31 Aug 2007, 05:29
Thanks so much guys for the help. I think probability will always be my weakness.

This problem was emailed to me with OA=1/3 (which is very close all of your answers), but I agree, the numbers might not be correct.
  [#permalink] 31 Aug 2007, 05:29
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There are 50 balls. 20 are red, 20 are green, 6 are blue, 4

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