ALEX Classroom Resource

  

Precalculus and Advanced Topics, Module 5, Topic A: Probability

  Classroom Resource Information  

Title:

Precalculus and Advanced Topics, Module 5, Topic A: Probability

URL:

https://www.engageny.org/resource/precalculus-and-advanced-topics-module-5-topic-a

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

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.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II
45 ) (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. [S-CP8]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II
46 ) (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [S-CP9]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
49 ) (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. [S-CP8]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
50 ) (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [S-CP9]

Tags: combinations, fundamental counting principle, independent events, multiplication rule, permutations, probability
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Comments

There are four lessons on this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site. 

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.

  This resource provided by:  
Author: Hannah Bradley