Probability

Lesson 2

Math

Unit 8

10th Grade

Lesson 2 of 10

Objective


Determine the probability of events with 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.A.4 — Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
  • 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.
  • 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.5
  • 7.SP.C.6

Criteria for Success


  1. Describe the outcomes of an event as “equally likely” or “fair” when each outcome has the same chance of occurring. 
  2. Describe what it means for an event to be “mutually exclusive,” that is, when $$P(A \space and \space B)=0$$, meaning the chance of $$A$$ occurring and the chance of $$B$$ occurring at the same time is impossible. 
  3. 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 $$P(A,B)$$.
  4. Calculate the probability of a mutually exclusive event of $$P(A \space or \space B)=P(A)+P(B)$$.
  5. Calculate the compound probability of a mutually exclusive event of $$P(A,B)=P(A)∙P(B)$$.
  6. Describe that the long-running frequency of an event (e.g., spinning a spinner 1,000 times vs. 10 times) will increase the chance that the probability of the event occurring matches the theoretical probability. 

Tips for Teachers


  • This is the first lesson out of 2 that focuses on finding the probability of mutually exclusive events. This lesson focuses on the probability of events with replacement, while Lesson 3 focuses on the probability of events without replacement. 
  • The guiding questions for Anchor Problem #1 are key to remembering and synthesizing basic probability terms and concepts.
  • The following resources may be helpful to understand mutually exclusive events. 
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Anchor Problems

25-30 minutes


Problem 1

Below is a spinner with four quadrants, each labeled 1 through 4. Each outcome is equally likely.

Sam spins the spinner twice and doesn't land on 4. What is the probability of this occuring?

Guiding Questions

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Problem 2

Dan has shuffled a deck of cards. He chooses a first card, looks at it, puts the card back into the deck, shuffles again, and finally 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

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 a card from the card bag (four blue cards and two red cards). Record the number from your spin and the color of the card selected.

  1. Why is the probability of the event “spinning an odd number and randomly selecting a blue card” not the same as the probability of the event “spinning an even number and randomly selecting a blue card”? Which event would have a great probability of occurring and why?
  2. Why is the probability of the event “spinning an odd number and randomly selecting a blue card” not equal to the probability of “spinning an odd number or randomly selecting a blue card”?

References

EngageNY Mathematics Algebra II > Module 4 > Topic A > Lesson 1Exit Ticket, Question #1 and #2

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.

Next

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

Lesson 3
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Lesson Map

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

Topic A: Conditional Probability and the Rules of Probability

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