The obvious answer, that there are eight balls of each color, doesn’t quite work: Of the 120 possible pairs drawn from such a bag, 64 have one ball of each color (8 white balls × 8 black balls) and 56 have two of the same color (28 possible pairs of white balls + 28 possible pairs of black balls). That gives a probability of 64/120 = 0.53 of getting a mixed draw and 56/120 = 0.47 of getting two balls of the same color.

But if the bag contains 6 balls of one color and 10 of the other, then there are 60 ways of getting a mixed draw, 45 ways of drawing the more common color, and 15 ways of drawing the less common color. 60 = 45 + 15, so the two outcomes are equally likely.