Let's learn about expected value. We'll start by calculating the average value of a goal. Here, our goal is to draw a star. The reward is the face value of the card. We have three possible reward outcomes. 1 2 and three. To find the average point value, we add up all the possible values and divide by the number of outcomes. So, 1 + 2 + 3 is 6. Then, because there are three possible outcomes, we divide 6 by 3. The average point value for this goal is two.
Let's look at a different scenario. If a goal is missed, then zero points are awarded. For this goal, we only get points if we draw a circle. So, the possible rewards are two points, 0 points, or four points, giving us three outcomes. To find the average reward, we sum the reward for each outcome and divide by the number of outcomes. So, 2 + 0 + 4 equals 6. Then, we divide by the three possible outcomes. 6 / 3 equals 2.
So, the average point value for this goal is two points. A goal's average reward is the sum of the points in each outcome divided by the number of possible outcomes. Drawing a card that doesn't fit the goal awards zero points.
Let's calculate the average point value of this goal. First, we add the possible point values together. Since our goal is to get a square card, the first card awards zero points. The second card awards one point, and the third card awards two points. Then we divide by the number of outcomes which is three. So 3 divided by 3 equals 1. The average point value for this goal is one point.
Let's do one more. This time with four possible outcomes. The goal is to draw a star. Drawing each of these cards awards two points, zero points, four points, and zero points respectively. Adding these up gives us six. Then we divide by the total number of outcomes which is four. 6 / 4 equals 1.5. So the average point value is 1.5.
This process of finding the average value of an event across all of its possible outcomes is called the expected value. The expected value tells us what we can expect the average outcome to be if we repeat the event many times.
