Describe the error in finding DE Point D is the centroid ABC

You didn't mention if the balls drawn with or without replacement.
However I will give you both probabilities

A) Ball drawn and replaced before the second draw:

Sample size = {7 Red, 9 Black, 3 White} = 19 possible outcomes
Favorable outcome={drawing black ball}

P( 1st black draw) = 9/19 = 0.4736
P( 2nd black draw) = 9/19 = 0.4736

P( 1st black draw AND 2nd black draw ) =0.4736 x 0.4736 = 0.224

B) Ball drawn and not replaced:

P(1st black draw) = 9/19 = 0.4736.

Now that one black is drawn and not replaced, then the remaining number of black is now 8 and the total 18 instead of 19:

P( 2nd black draw) = 8/18 = 0.4444
P( 1st black draw AND 2nd black draw without replacement)=

0.4736. x  0.4444 = 0.21