Probability

Lesson 3

Math

Unit 8

10th Grade

Lesson 3 of 10

Objective


 Determine the probability of events without replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 7.SP.C.6

Criteria for Success


  1. Describe events “without replacement” as events where the first event affects the outcome of the second event.
  2. Describe when an event is dependent (without replacement), and when it isn’t.
  3. Describe the outcomes of an event as “equally likely” or “fair” when each outcome has the same chance of occurring.
  4. Use a tree diagram to describe the sample space of a chance experiment when events are mutually exclusive and identify $$P(A)$$, $$P(A \space or\space B)$$, $$P(not A)$$, and $$P(A,B)$$.
  5. Calculate the probability of a mutually exclusive event of $$P(A \space or \space B)=P(A)+P(B)$$.
  6. Calculate the compound probability of a mutually exclusive event of $$P(A,B)=P(A)∙P(B)$$.

Tips for Teachers


  • This is the second lesson out of two that focuses on finding the probability of mutually exclusive events. This lesson focuses on the probability of events without replacement, while Lesson 2 focused on the probability of events with replacement. 
  • This lesson will prepare students to access S-CP.3 standard, which introduces the idea of conditional probability, which will be addressed in Lesson 5. 
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Anchor Problems


Problem 1

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:

  • Pull a cube from the bag and put it on the table.
  • Pull a second cube from the bag and put it on the table.
  • If the cubes are different colors, then Player A wins.
  • If the cubes are the same color, then Player B wins. 

Is this game fair? How do you know? 

Guiding Questions

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Problem 2

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? 

Guiding Questions

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Target Task


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). 

  1. What is the probability of spinning an even number and choosing two blue cards? 
  2. If you selected and recorded the color of the first card and then placed the card back into the bag before choosing the second card, how would your probability change? 

References

EngageNY Mathematics Algebra II > Module 4 > Topic A > Lesson 1Scenario 1

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..

Modified by Fishtank Learning, Inc.

Additional Practice


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.

  • Include problems from the Problem Set Guidance in Lesson 2 that were not used.
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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Conditional Probability and the Rules of Probability

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