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

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Current Student
Joined: 11 May 2008
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There are 20 red marbles, 20 blue marbles, 5 white marbles, [#permalink]

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22 Jul 2008, 07:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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Director
Joined: 01 Jan 2008
Posts: 618

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22 Jul 2008, 07:43
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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SVP
Joined: 30 Apr 2008
Posts: 1867

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Location: Oklahoma City
Schools: Hard Knocks

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22 Jul 2008, 07:44
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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Last edited by jallenmorris on 22 Jul 2008, 07:48, edited 2 times in total.

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Current Student
Joined: 11 May 2008
Posts: 555

Kudos [?]: 222 [0], given: 0

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22 Jul 2008, 07:44
good one ... tis correct

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Director
Joined: 27 May 2008
Posts: 541

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22 Jul 2008, 07:49
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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Current Student
Joined: 12 Jun 2008
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Schools: INSEAD Class of July '10

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22 Jul 2008, 07:52
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

Kudos [?]: 58 [0], given: 0

Re: probability, good one   [#permalink] 22 Jul 2008, 07:52
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