A probability tells us about the chance of one event occurring, while an expected value is the weighted average of all possible outcomes of an experiment.
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To describe the difference between an expected value and a probability, let's begin by comparing the definitions of these two concepts.
Must be a number between 0 and 1, inclusive. Often it is expressed as a decimal or a percent.
Can be any number and does not have to be a possible outcome.
Therefore, an expected value involves using the probabilities, because there are weights in a weighted average. Let's consider an example to better illustrate this relationship.
Example
Assume that we roll a die one time.
If a die is fair, then the probability of rolling each number from the following set of possible outcomes will be constant.
{ 1,2,3,4,5,6}
Since we have 6 possible outcomes, the probability of rolling 1 chosen number will be 1 6. Next, if we would like to evaluate the expected value of rolling a die we should add the products of each outcome and its corresponding probability of occuring.
