CK-12-Pre-Calculus Concepts

15.2. Expected Value and Payoffs http://www.ck12.org

15.2 Expected Value and Payoffs

Here you will apply what you know about mean and averages to weighted averages and expected value.
When playing a game of chance there are three basic elements. There is the cost to play the game (usually), the
probability of winning the game, and the amount you receive if you win. If games of chance with these three
elements are played repeatedly, you can use probability and averages to calculate how much you can expect to win
or lose in the long run.
Consider a dice game that pays you triple your bet if you roll a six and double your bet if you roll a five. If you roll
anything else you lose your bet. What is your expected return on a one dollar wager?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/62531

http://www.youtube.com/watch?v=j__Kredt7vY Khan Academy: Expected Value

Guidance

A weighted average is like a regular average except the data is often given to you in summary form.
Data in Raw Form:
1, 3, 5, 3, 2, 1, 2, 5, 6, 4, 5, 2, 6, 1, 4, 3, 6, 1, 2, 4, 6, 1, 3, 1, 3, 5, 6
Data in Summary Form:

TABLE15.1:

Number Occurrence Count

1 6

2 4

3 5

4 3

5 4

6 5

Total Occurrences: 27

Notice that the summary data indicates, for example, how many times a 1 was rolled (6 times). To calculate the total
number of occurrences of data:

• In raw form: count how many data points you have