For example, you might roll (1, 1), which notates one on the first die and one on the second die. A total of 36 different outcomes can appear when you roll two dice. Let’s do this step by step.įirst, list out all of the possible outcomes. For example, you could calculate the expected value of rolling a pair of weighted dice.
You can use these steps to calculate more sophisticated expected values. The expected value was then just the sum of the values in step 2 multiplied by the probabilities in step 3. Calculated the probability that each outcome occurred.Determined the value of each outcome (here just the value of the die).Listed out all of the possible outcomes.Notice that we did the same three things to calculate both of these expected values. If you rolled a loaded die an infinite number of times, the average outcome would be 4.125, which is higher than what you would expect from a fair die. Hence, the expected value of a loaded die does not equal the average value of its outcomes. The expected value of a random event is a type of weighted average it is the sum of each possible outcome of the event, weighted by the probability that each outcome occurs:Į(x) = \sum_\\