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There are 20 red marbles, 20 blue marbles, 5 white marbles,

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There are 20 red marbles, 20 blue marbles, 5 white marbles, [#permalink] New post 22 Jul 2008, 06:39
There are 20 red marbles, 20 blue marbles, 5 white marbles, and 5 green marbles in a bag. If two balls are to be selected at random, without replacement, what is the probability of getting two balls with the same color?
A. 4/7
B. 19/25
C. 16/49
D. 32/49
E. 32/50
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Re: probability, good one [#permalink] New post 22 Jul 2008, 06:43
arjtryarjtry wrote:
There are 20 red marbles, 20 blue marbles, 5 white marbles, and 5 green marbles in a bag. If two balls are to be selected at random, without replacement, what is the probability of getting two balls with the same color?
A. 4/7
B. 19/25
C. 16/49
D. 32/49
E. 32/50


(C(20,2)+C(20,2)+C(5,2)+C(5,2))/C(50,2)=16/49 -> C
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Re: probability, good one [#permalink] New post 22 Jul 2008, 06:44
16/49

i did

Chance to same color for each color = (\frac{20}{50}*\frac{19}{49})*2 + (\frac{5}{50}*\frac{4}{49})*2 (times 2 because there are 20 Red and 20 blue, so same numbers and same thing for White and Green with 5 each.

= \frac{76}{245} + \frac{4}{245} = \frac{80}{245} = \frac{16}{49}

Chance to select one
arjtryarjtry wrote:
There are 20 red marbles, 20 blue marbles, 5 white marbles, and 5 green marbles in a bag. If two balls are to be selected at random, without replacement, what is the probability of getting two balls with the same color?
A. 4/7
B. 19/25
C. 16/49
D. 32/49
E. 32/50

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Last edited by jallenmorris on 22 Jul 2008, 06:48, edited 2 times in total.
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Re: probability, good one [#permalink] New post 22 Jul 2008, 06:44
:lol: good one ... tis correct
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Re: probability, good one [#permalink] New post 22 Jul 2008, 06:49
arjtryarjtry wrote:
There are 20 red marbles, 20 blue marbles, 5 white marbles, and 5 green marbles in a bag. If two balls are to be selected at random, without replacement, what is the probability of getting two balls with the same color?
A. 4/7
B. 19/25
C. 16/49
D. 32/49
E. 32/50


Total balls = 20+20+5+5 = 50

P = RR + BB + WW + GG
= 20/50 * 19/49 + 20/50 * 19/49 + 5/50 * 4/49 + 5/50 * 4/49
= 800 / (50*49)
=16 / 49 ... option C
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Re: probability, good one [#permalink] New post 22 Jul 2008, 06:52
Total numbers of possibilities (ordered): 50x49

Possibilities for 2 red marbles: 20x19 = 380
Possibilities for 2 blue marbles: 20x19 = 380
Possibilities for 2 white marbles: 5x4 = 20
Possibilities for 2 green marbles: 5x4 = 20

--> Total number of favorable possibilities = 800

Answer is 800/(50x49) = 16/49

==> Answer is (C)
Re: probability, good one   [#permalink] 22 Jul 2008, 06:52
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