SOLUTION: a box contain a four red, three black, and five white marble. two marbles are randomly drawn from this box and the color of these marbles is observed. 1) write all the possible

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Question 758269: a box contain a four red, three black, and five white marble. two marbles are randomly drawn from this box and the color of these marbles is observed.
1) write all the possible observations.
2)calculate the probability of selecting two marbles of same color.
Answer by Theo(13342) About Me  (Show Source):
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you have 66 possible combinations of drawing 2 balls at a time taken from 12 balls.

this is calculated by the combination formula of 12C2.

12C2 = (12*11) / (2*1) = 6*11 = 66

the number of ways you can draw 2 red balls out of 4 = 4C2
the number of ways you can draw 2 black balls out of 3 = 3C2
the number of ways you can draw 2 white balls out of 5 = 5C2

4C2 equals (4*3) / (2*1) = 6
3C2 equals (3*2) / (2*1) = 3
5C2 equals (5*4) / (2*1 = 10

total ways you can get balls of the same color (either all red or all black or all white) equals 6 + 3 + 10 which equals 19.

the probability of getting all balls of the same color is therefore equal to 19 / 66.