This math unit introduces students to the fundamentals of probability, focusing on the concept of random variables. Initially, students learn to define experiments and random variables, and how to list outcomes in terms of the random variable. They progress to applying their understanding to specific values and sets of outcomes, such as analyzing lists of outcomes that satisfy certain conditions. The unit further develops proficiency in calculating probabilities using probability tables for various criteria—determining probabilities for less than, greater than, or equal to specific values, and identifying valid probability distributions that sum to one. Advanced topics include calculating expected values and evaluating financial decision-making scenarios based on expected gains or losses. Students also explore the concept of fairness in games by comparing ticket prices to expected prizes, culminating in adjusting parameters like prize values to balance the fairness in theoretical games. Throughout the unit, students enhance their ability to apply probabilistic concepts to practical and diverse situations, reinforcing their understanding of elementary probability and statistics.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.