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Can you explain? Another probability

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by mjjking » Thu Feb 26, 2009 1:42 am
A bag contains six marbles: two red, two blue, and two green. If two marbles are drawn at random, what is the probability that they are the same color?

1/10
1/14
3/7
1/5
2/9
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by bluementor » Thu Feb 26, 2009 2:14 am
Prob of picking any marble = 1

After picking the first marble, you are left with 5 marbles. Only 1 marble from these 5 will match the first one. Therefore:

Prob(2 same colored marbles) = 1 x (1/5) = 1/5

Choose D.

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by rsadana1 » Thu Feb 26, 2009 7:37 am
An alternate solution:

Total number of outcomes = Total ways of selecting 2 marbles from the given 6 marbles = 6C2 = 15

Desired outcomes = 2 balls of same color can be selected in following three ways:
Select both red balls = 2C2
Select both blue balls = 2C2
Select both green balls = 2C2

Now at a time we can either select both red balls OR both blue balls OR both green balls, so the desired number of outcomes = 2C2+2C2+2C2 = 1+1+1= 3

So probability = 3/15 = 1/5
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