Question 885679
Let's label the balls, so we can distinguish between balls of the same color.
I will label the red balls R1, R2, R3, and R4.
I will label the white balls W1, W2, and W3.
I will label the green balls G1, G2, and G3.
There are {{{10*9/2=45}}} sets of two balls that could be made from those 10 balls.
How many same color pairs can be made?
with the four red balls, we can make {{{4.3/2=6}}} sets of 2 red balls.
With the white balls, we can make 3 sets of two green balls.
With the green balls, we can make 3 sets of two green balls.
In all, we can make {{{6+3+3=12}}} sets of two balls of the sane color.
Those sets, as a fraction of all possible sets of teo balls are
{{{12/45=4/15}}} .
That {{{highlight(4/15)}}} is the probability that both balls are the same color.