Probability

Lesson 6

Math

Unit 8

10th Grade

Lesson 6 of 10

Objective


Determine whether events are independent. 

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.3 — Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
  • S.CP.A.5 — Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

Criteria for Success


  1. Define independent events as events whose probabilities of occurring does not affect one another. 
  2. Describe that there are two ways to determine independence of events:
    1. $$A$$ and $$B$$ are independent events if $$P(B│A)=P(B)$$ and $$P(A│B)=P(A)$$.
    2. $$A$$ and $$B$$ are independent events if $$P(A \space and \space B)=P(A)∙P(B)$$.
  3. Interpret contextual situations by determining independence and calculating the conditional probability. 
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Anchor Problems


Problem 1

You are in a diner and want to know if choosing cream or sugar are independent events, that is, if one depends on the other. Below is a Venn diagram that represents the number of people in the diner one morning. A random person is chosen.

 

  1. Is this random person more likely to have cream in his coffee if he has sugar? Calculate the probability.
  2. Is this random person more likely to have sugar in his coffee if he has cream? Calculate the probability

Guiding Questions

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Problem 2

A coin is tossed and a single six-sided die is rolled. If landing on heads is represented by $$H$$ and rolling a $$3$$ is represented by $$R$$, determine if the following is true:

$$P(H \space and \space 3)=P(H)\cdot P(3)$$

 

Guiding Questions

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Target Task


Today there is a 55% chance of rain, a 20% chance of lightning, and a 15% chance of lighting and rain together. Are the two events “rain today” and “lightning today” independent events? Justify your answer. 

References

Illustrative Mathematics Rain and Lightning.Part a

Rain and Lightning., accessed on June 15, 2017, 8:52 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

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.

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Lesson 5

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Lesson 7

Lesson Map

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Topic A: Conditional Probability and the Rules of Probability

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