SOLUTION: A bag contains 12 red and 8 blue marbles. If you randomly select 2 marbles, what is the probability that they are the same color? I feel like this is an nPr or a nCr, but I am

Algebra ->  Probability-and-statistics -> SOLUTION: A bag contains 12 red and 8 blue marbles. If you randomly select 2 marbles, what is the probability that they are the same color? I feel like this is an nPr or a nCr, but I am      Log On


   

Question 731105: A bag contains 12 red and 8 blue marbles. If you randomly select 2 marbles, what is the probability that they are the same color?
I feel like this is an nPr or a nCr, but I am unsure.
Found 3 solutions by lynnlo, ikleyn, greenestamps:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53419) About Me  (Show Source):
You can put this solution on YOUR website!
.
A bag contains 12 red and 8 blue marbles. If you randomly select 2 marbles, what is the probability
that they are the same color?
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P = P(red,red) + P(blue,blue) = %2812%2F20%29%2A%2811%2F19%29 + %288%2F20%29%2A%287%2F19%29 = %2812%2A11%2B8%2A7%29%2F%2820%2A19%29 = 188%2F380 = 47%2F95 = 0.4947  (rounded).    ANSWER

Solved.

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The answer in the post by @lynnlo is incorrect.
Simply ignore his post.



Answer by greenestamps(13258) About Me  (Show Source):
You can put this solution on YOUR website!


It's an nCr problem and not an nPr problem, because order does not matter.

The total number of possible outcomes is choosing 2 of the 20 marbles: 20C2.

The favorable outcomes are choosing 2 of the 12 red marbles AND 0 of the 8 blue marbles OR 2 of the blue marbles AND 0 of the 12 red marbles. Note that the "AND"s indicate multiplication and the "OR"s indicate addition:

(12C2 * 8C0) + (8C2 * 12C0).

%28C%2812%2C2%29%2AC%288%2C0%29%2BC%288%2C2%29%2AC%2812%2C0%29%29%2FC%2820%2C2%29

%2866%2A1%2B28%2A1%29%2F190=94%2F190=47%2F95

Or you can get the answer without using nCr, by looking at the probabilities of picking one marble at a time, as the other tutor does.