In Module 5, Topic A, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that can be used to calculate the probability of the intersection of two events in situations where the two events are not independent (S-CP.B.8). Students are also introduced to three techniques for counting outcomes—the fundamental counting principle, permutations, and combinations (S-CP.B.9). Students consider the distinction between combinations and permutations and identify situations where it would be appropriate to use each of these methods. For example, in Lesson 4 students are presented with a scenario involving 20 singers auditioning for a high school musical and a director who must choose two singers for a duet, as well as two singers to perform lead and backup. To answer the question, students have to indicate whether or not the scenario involves a permutation or combination. In the final lesson of this topic, students use the fundamental counting principle, permutations, and combinations to calculate probabilities, and these probabilities are interpreted in context. In Lesson 4, students must explain how to determine the probability (either using a permutation or combination) that a 4-digit passcode could be 1234 if the digits in the code cannot repeat.
Note: Although this module is identified as Precalculus and Advanced Topics in the EngageNY curriculum, it corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses of Study.