16 # 16 - Probability

The study of probability arises naturally in a variety of situations. Games in which we flip coins, roll dice, spin spinners, or pick cards all have an element of chance. We don’t  know what the spinner will land on, and we don’t know how the dice will roll. This elemento of chance adds excitement to the game and makes it easy to design class activities and problems that present probability in a way that can be fun for students to learn.

If probability were used only in analyzing games of chance, it would not be an importante subject. But probability has far wider applications. In business and finance, probability can be used in determining how best to allocate assets. In medicine, probability can be used to determine how likely it is that a person actually has a certain disease, given the outcomes of test results.

In this course, we focus on the following topics and practices within the Common Core State Standards for Mathematics (CCSSM).

Standards for Mathematical Content in the CCSSM In the domain of Statistics and Probability, students learn that the probability of a chance event expresses the likelihood that the event will occur. They collect data on chance processes and they recognize that the fraction of times an event is observed to occur approximates the event’s probability. They find probabilities, including those for compound events. They use organized lists, tables, and tree diagrams to display and analyze compound events and to determine their probabilities.

Standards for Mathematical Practice in the CCSSM

Opportunities to engage in all eight of the Standards for Mathematical Practice described in the CCSSM occur throughout the study of probability, although the following standards may be especially appropriate for emphasis:

• 1 Make sense of problems and persevere in solving them. Students engage in this practice when they solve challenging probability problems, both practical and whimsical.

• 2 Reason abstractly and quantitatively. Students engage in this practice when they use the definition of multiplication in reasoning about compound events and when they capitalize on the relationship between the long term relative frequency of an event and its theoretical probability, applying it in both directions.

• 4 Model with mathematics. Students engage in this practice when they make a probability model for a chance process and use it to make predictions about likelihoods of events.

(From Common Core Standards for Mathematical Practice. Published by Common Core Standards Initiative.)