The probability of three reds is: c (3,5)/c (3,9) =10/84 = 5/42.

The probability of "three whites" is c (3,4)/c (3,9) = 4/84 = 2/42.

The probability of two reds and one white is: c (2,5) * c (1,4)/c (3,9) = 20/42.

The probability of two whites and one red is: c (1, 5) * c (2,4)/c (3,9) =15/42.

Three reds or three whites cannot be copied. The probability of two reds and one white is 3/5, and the probability of two whites and one red is 3/5.

So the probability that three balls are not the same number is: (15/42+20/42) * (3/5) =1/2.