Curriculum / Math / 10th Grade / Unit 8: Probability / Lesson 3
Math
Unit 8
10th Grade
Lesson 3 of 10
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Lesson Notes
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Determine the probability of events without replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
The core standards covered in this lesson
S.CP.A.2 — Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S.CP.B.6 — Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
S.CP.B.7 — Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
S.CP.B.8 — 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.
7.SP.C.7 — Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
The foundational standards covered in this lesson
7.SP.C.6 — Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
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
Allison has put together a simple game. She put 6 cubes in a paper bag—3 yellow and 3 blue. Allison has determined that the rules are as follows:
Is this game fair? How do you know?
Dan has shuffled a deck of cards. He chooses the first card and places it on the table. He shuffles again and chooses a second card. What is the probability that Dan’s two cards are of the same suit?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Use the game scenario to answer the following questions.
Game Tools: Spinner 1 (three equal sectors with the number 1 in one sector, the number 2 in the second sector, and the number 3 in the third sector) Card bag (Blue-A, Blue-B, Blue-C, Blue-D, Red-E, Red-F)
Directions: Spin Spinner 1 and randomly select two cards from the card bag (four blue cards and two red cards).
Algebra II > Module 4 > Topic A > Lesson 1 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..
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
Determine the probability of events that are not mutually exclusive to formalize the addition rule.
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
7.SP.C.7S.CP.A.2S.CP.B.6S.CP.B.7S.CP.B.8
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
Describe and apply the counting principle and permutations to contextual and non-contextual situations.
S.CP.B.9
Describe and apply the counting principle and combinations to contextual and non-contextual situations.
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