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?

2.75

Step-by-step 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