# Expected Value

## What is Expected Value?

Expected value is a statistical concept that represents the average outcome of a probability distribution. It is calculated by multiplying the value of each possible outcome by its probability and then summing the results.

For example, suppose you have a bag with three marbles: one red, one blue, and one green. The probability of drawing a red marble is 1/3, the probability of drawing a blue marble is 1/3, and the probability of drawing a green marble is 1/3. If the value of a red marble is \$5, the value of a blue marble is \$10, and the value of a green marble is \$20, the expected value of the bag would be calculated as follows:

Expected value = (1/3 x \$5) + (1/3 x \$10) + (1/3 x \$20) = \$10

In this example, the expected value represents the average amount of money you can expect to get if you draw a marble from the bag multiple times. It does not mean that you will always get exactly \$10 – you may get more or less depending on the actual outcome – but over time, the average value of your draws will tend towards the expected value.

Expected value is a useful concept for understanding and analyzing probability distributions, and can be used in a variety of contexts, such as decision-making, risk assessment, and financial modeling.