1. Expected Value Expected value can be thought of as an average over time . When rolling dice, it is unrealistic to expect a 7 every time. However, 7 is the expected value for a roll of two dice. This means that after many rolls, the average should lie around 7. The dice are equally as likely to come up as a 6 as an 8. Likewise for 5 & 9, 4&10, 3 &11, 2 & 12.

2. Expected Value How do we calculate expected value? If the dice obeyed probability perfectly, after 36 rolls we would have the following: One 2, two 3’s, three 4’s, four 5’s, five 6’s, six 7’s, five 8’s, four 9’s, three 10’s, two 11’s, and one 12. If we were to average these values, we would find the expected value :

3. Expected Value If ten $1 bills, three $5 bills, and one $100 bill are placed in a hat and drawn at random, what is the expected value of playing this game? If we play this game repeatedly, we would win an average of $8.93 per game.

4. % Error % Error refers to the difference between an actual mean outcome and the expected value. For yesterday’s dice rolling activity, the average value was 7.120, as opposed to the expected value of 7.