## Expected Values

**Overview:**

The expected value is the average of the probability model. It can be used to calculate the expected sales of an object, expected winnings or expected trials using probabilities.

**Expected Value of Random Variables**

You find the expected value of random variables using the following steps:

1. Multiply each value by its probability

2. Find the sum of these values

It’s simple! This is the most common expected variable problem. You can also do this on your calculator using these steps:

1. Insert the values into L1 and the probabilities into L2

2. Press the STAT button, tab over to CALC and select 1:1-VarStats. Use lists L1 and L2. The value is the expected value.

**Expected Value of the Geometric Model**

In a geometric probability model the expected value can be found using the following equation:

Where is probability of success.

In a geometric probability model the expected value can be found using the following equation:

**Expected Value of the Binomial Model**In a geometric probability model the expected value can be found using the following equation:

Where is probability of success and is the number of trials

A commuter must pass through 5 traffic lights on her way to work. Below is the probability model for the number of lights she will hit. How many reds can she expect to hit?

**Example: 1.**A commuter must pass through 5 traffic lights on her way to work. Below is the probability model for the number of lights she will hit. How many reds can she expect to hit?

The commuter can expect to hit about 2.25 lights.