Explanation:
that means 2 blue or 2 red or 2 green.
12 marbles in total.
when the first marble is picked, there are only 11 left.
a probability is always the ratio of
desired cases / totally possible cases
the probabilty to pull first a blue marble is
5/12 = 0.416666666...
if that is the case, then the probabilty for the second marble to be blue too is
4/11 = 0.363636363...
(there are only 4 blue marbles in a total of 11 marbles).
and the probabilty for getting 2 blue marbles is
5/12 × 4/11 = 20/132 = 5/33 = 0.151515151...
the probabilty to pull first a red marble is
4/12 = 1/3 = 0.333333333...
if that is the case, then the probabilty for the second marble to be red too is
3/11 = 0.272727272...
(there are only 3 red marbles in a total of 11 marbles).
and the probabilty for getting 2 red marbles is
1/3 × 3/11 = 3/33 = 1/11 = 0.0909090909...
the probabilty to pull first a green marble is
3/12 = 1/4 = 0.25
if that is the case, then the probabilty for the second marble to be green too is
2/11 = 0.181818181...
(there are only 2 green marbles in a total of 11 marbles).
and the probabilty for getting 2 green marbles is
1/4 × 2/11 = 2/44 = 1/22 = 0.045454545...
the probabilty to have any of these 3 mutually exclusive cases (to get a pair of the same color) is the sum of the probabilities :
0.151515151... + 0.09090909... + 0.045454545... =
5/33 + 1/11 + 1/22 = 10/66 + 6/66 + 3/66 = 19/66 =
= 0.287878787...