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

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VP
Joined: 10 Jun 2007
Posts: 1465
Followers: 6

Kudos [?]: 133 [0], given: 0

There are 50 balls. 20 are red, 20 are green, 6 are blue, 4 [#permalink]  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
Joined: 06 Mar 2006
Posts: 497
Followers: 7

Kudos [?]: 91 [0], given: 1

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
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

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
Joined: 22 Aug 2007
Posts: 572
Followers: 1

Kudos [?]: 14 [0], given: 0

Re: Probability [#permalink]  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.
CEO
Joined: 29 Mar 2007
Posts: 2591
Followers: 16

Kudos [?]: 234 [0], given: 0

Re: Probability [#permalink]  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

801/2450 or 401/1225
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 63 [0], given: 7

Re: Probability [#permalink]  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
Joined: 10 Jun 2007
Posts: 1465
Followers: 6

Kudos [?]: 133 [0], given: 0

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.
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