Question

A box contains 5 Balls labeled with the number "1", 3 balls labeled with the number "2", and 1 ball labeled with the number "3". Two balls are selected, without replacement. Let X be the total of the values on the two balls. Find the mean of X.

Answer 1

If both balls are numbered 1, there are 5C2 = 10 ways of that happening and the sum is 2.

If both balls are numbered 2, there are 3C2 = 3 ways of that happening and the sum is 4.

If one ball is numbered 1 and the other is numbered 2, there are 5*3 = 15 ways of that happening and the sum is 3.

If one ball is numbered 1 and the other is numbered 3, there are 5*1 = 5 ways of that happening and the sum is 4.

If one ball is numbered 2 and the other is numbered 3. there are 3*1 = 3 ways of that happening and the sum is 5.

Mean = (10*2 + 3*4 + 15*3 + 5*4 + 3*5) / (10 + 3 + 15 + 5 + 3) = 112 / 36 = 3.11.