What is the expected mean of ten throws of a 20-sided dice?

Answer 1

Hi Lucy!

We’ll assume that the die is equally weighted so that the probability of throwing any one of the numbers 1, 2, up through 20 is 1/20.

The expected mean for one throw is found by looking at each of the 20 sides and multiplying the probability by the number showing, then adding them up like this:

1/20 * 1 + 1/20 * 2 + 1/20 * 3 + ... + 1/20 * 20

A shorter way to do this is to factor out 1/20 so that we get

1/20 (1+2+3+...+20)

The answer is 10.5, which is what we expect from a single throw.

We might have guessed this anyway, since 10.5 is exactly in the middle of the numbers 1 through 20.

For 10 throws, the expected mean is 10 * 10.5 = 105.

Please let me know if I can be more helpful!

Joe