Curriculum / Math / 10th Grade / Unit 8: Probability / Lesson 9
Math
Unit 8
10th Grade
Lesson 9 of 10
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Lesson Notes
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Describe and apply the counting principle and permutations to contextual and non-contextual situations.
The core standards covered in this lesson
S.CP.B.9 — Use permutations and combinations to compute probabilities of compound events and solve problems.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Using the digits 1, 2, and 3, write an expression to answer the following questions
Your phone requires you to use five numbers for the code, but you only can use numbers 1-5 for the code.
The first combination you come up with is:
You then realize how "insecure" this number might be since anyone could guess it. Figuring this out you wonder, "How many possibilities are there for combinations if I only use each number once?"
You change the phone settings so that you only need a three-digit code to open the lock.
This means you have 5 numbers to choose from and 3 positions to put those numbers in, which is represented by $$_5P_3$$. How many different combinations can you get if you have three positions and a choice of five numbers with no repetition?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The combination for a lock consists of three numbers.
Precalculus and Advanced Topics > Module 5 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Jacqui is putting together sets of greeting cards for a school fundraiser. There are four different card options, two different colored envelopes, and four different sticker designs. A greeting card set consists of one type of card, one color for the envelopes, and one sticker design. How many different ways can Jacqui arrange the greeting card sets? Explain how you determined your answer.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Describe and apply the counting principle and combinations to contextual and non-contextual situations.
Topic A: Conditional Probability and the Rules of Probability
Describe the sample space of an experiment or situation. Use probability notation to identify the “and,” “or,” and complement outcomes from a given sample space.
Standards
7.SP.C.8S.CP.A.1
Determine the probability of events with replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
7.SP.C.7S.CP.A.2S.CP.A.4S.CP.B.6S.CP.B.7
Determine the probability of events without replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
7.SP.C.7S.CP.A.2S.CP.B.6S.CP.B.7S.CP.B.8
Determine the probability of events that are not mutually exclusive to formalize the addition rule.
S.CP.A.1S.CP.A.2S.CP.B.7
Describe conditional probability and develop the rule $$P(B|A)=\frac{P(A \space \mathrm{and} \space B)}{P(A)}$$.
S.CP.A.3
Determine whether events are independent.
S.CP.A.2S.CP.A.3S.CP.A.5
Calculate and analyze relative frequencies in two-way tables to make statements about the data and determine independence.
S.CP.A.4S.CP.A.5S.ID.B.5
Make decisions about medical testing based on conditional probabilities.
S.CP.A.3S.CP.A.4S.CP.A.5
S.CP.B.9
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