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Applications of Probability

Applications of Probability

In this chapter, students will study the fundamental concepts and rules of probability. In the beginning, students will be introduced to several definitions: an event and its complement, an outcome and sample space, and a probability experiment and its elements. From there, the difference between experimental and theoretical probability will be explained. Unions and intersections of two or more events will be taught with the usage of Venn diagrams. Students will learn that the occurrence of some events can affect the occurrence of other events, and investigating that fact will help them discover the difference between dependent and independent events. Students will be encouraged to explore the connection between independence and conditional probability, then analyze a variety of conditional situations modeled by tree diagrams, frequency tables, and Venn diagrams. Numerous real-life situations will be presented and analyzed from the perspective of independence and conditional probability. One of the lessons is deeply focused on geometric probability problems in one-, two-, and three-dimensional situations. Students will also learn to interpret data given in two-way frequency tables and to calculate joint, marginal, and conditional relative frequencies. Students will practice using the Addition and Multiplication Rules of Probabilities when calculating the probabilities of compound events. The concepts of permutations, combinations, and simulations will be introduced and connected to the computation of probabilities. Students will be taught how calculating probabilities of events helps to choose between different decision-making methods and whether or not decisions made using those methods are fair. Finally, strategizing and decision-making principles will be explored and put into practice through different concepts of probability.