Question

A fair, 12-sided die has numbers on each of its faces. There are three faces with a 1, three faces with a 2, one face with a 3, four faces with a 4, and one face with a 5.

What is the expected value when rolling this die?

Answer 1

2.75

Explanation:

Let's start by making a frequency table. If there is one face, you have a 1/12 chance of getting the value--that's what the "frequency" column means.

Face Frequency

1 3/12

2 3/12

3 1/12

4 4/12

5 1/12

Now to get E(X) we need to multiply each face by the frequency of it occuring and add all these together:

E(X) = 1(3/12) + 2(3/12) + 3(1/12) + 4(4/12) + 5(1/12)

= 2.75