Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Let's separate into 3 cases:
Note that we put the number of color balls we want in the numerator and the total number of color balls remaining in the denominator.
Case 1: 2 blue marbles
[tex]\frac{5}{13} * \frac{4}{12} = \frac{5}{39}[/tex]
(There were 5 blues originally, and 4 blues after 1 blue is taken out, same logic but different colors and values in case 2 and 3.)
Case 2: 2 red marbles
[tex]\frac{6}{13} * \frac{5}{12} = \frac{5}{26}[/tex]
Case 3: 2 green marbles
[tex]\frac{2}{13} * \frac{1}{12} = \frac{1}{78}[/tex]
Now add up all 3 cases and you will have the probability as required.
[tex]\frac{5}{39} +\frac{5}{26}+ \frac{1}{78} = \frac{1}{3}[/tex]
