Party A, Party B and Party C decide the duty order by touching the ball.

It doesn't matter who comes first. No one suffers, and no one is cheap. Let's think about it first: if A, B and C touch the ball in turn, A won't look first. There is no doubt that everyone is 1/3, right? So if A looks first, will it affect the color of the balls in B and C's hands? Obviously, it will not affect. Is that understandable?

Then calculate:

1) A gets the red ball. But when he took the ball, there were three balls in his bag. The probability of getting the red ball is 1/3, right? It can be seen that he is not cheap

2) If Party B gets the red ball, it must get the white ball, and the probability of Party A getting the white ball is 2/3. Then the probability of Party B getting the red ball is 1/2. These two conditions must be met at the same time, so the probability of Party B getting the red ball is 2/3 * 1/2 = 1/3! There is no bargaining or loss.

3) No calculation is required. The remaining 1/3 is the probability that C gets the red ball.