Heavy black ball?

Let $r$ , $b$ , and $w$ be the weights of the red, black and white balls respectively.

Initially there are six possibilities, each with the same probability:

• $r > b > w$
• $r > w > b$
• $w > b > r$
• $w > r > b$
• $b > r > w$
• $b > w > r$

Then we find that red weighs more than white, which rules out the third, fourth and last possibilities.

So, we are left with three possibilities all equally likely:

• $r > b > w$
• $r > w > b$
• $b > r > w$

Two out of three of these involve black being heavier than white.

Therefore, there is a $\boxed{\frac{2}{3}}$ probability that the black ball is heavier than the white one.

Let the weight of the balls are $W_1,W_2,W_3$ with $W_1 > W_2 > W_3$

It is given that red ball is heavier than than white ball .

So. we can assign colors like below

From three cases where red ball is heavier than white there are two cases where black ball is heavier than white also

So, probability is $\dfrac{2}{3}$