In Module 5, Topic A, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this topic, students develop an understanding of the information that a probability distribution provides and interpret probabilities from the probability distribution of a discrete random variable in context (S-MD.A.1). Students work with different representations of probability distributions, using both tables and graphs to represent the probability distribution of a discrete random variable. Lessons 7 and 8 introduce the concept of expected value, and students calculate and interpret the expected value of discrete random variables in context. For example, in Lesson 7, students explore the concept of expected value by playing a game called Six Up, where the first player to roll 15 sixes wins. Students play the game, create a probability distribution, and use the data to calculate the mean of the distribution or expected value. In Lesson 8, students are given a probability distribution for the results of a donation drive for a cancer charity and use the distribution to calculate the expected value for the amount of money donated and interpret the value in context (S-MD.A.2).
Once students have developed an understanding of what the probability distribution of a discrete random variable is and what information it provides, they see in Lessons 9 and 10 that probabilities associated with a discrete random variable can be calculated given a description of the random variable (S-MD.A.3).
In the final lessons of this topic, students also see how empirical data can be used to approximate the probability distribution of a discrete random variable (S-MD.A.4). For example, in Lesson 12 students play a game where they toss two dice, find the absolute difference of the numbers on the two faces, and move the same number of places on a number line. The first player to move past 20 wins the game. Students carry out simulations of the game and use the estimated probabilities to create a probability distribution which is then used to determine the expected value.