Probability and Statistical Inference

Lesson 4

Math

Unit 8

11th Grade

Lesson 4 of 13

Objective


Determine when events are independent and describe independent events using everday language.

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.

Foundational Standards

  • 7.SP.C.8

Criteria for Success


  • Describe how to determine independence of events using both conditional probability and the intersection of two probabilities. 
  • Use the concept that if $${P(B|A)=P(B)}$$ and if $${P(A|B)=P(A)}$$, then $$A$$ and $$B$$ are independent, to determine independent events. 
  • Use the concept that if $$P(B\space\mathrm{and}\space A)=P(B)\cdot P(A)$$ then, $$A$$ and $$B$$ are independent. 

Tips for Teachers


The blog post, Teaching Probability Day 7 - Conditional Probability by Slightly Skewed uses LearnZillion and is useful context.

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Anchor Problems

25-30 minutes


Problem 1

Back to the diner! 

You 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. Is this random person more likely to have cream in his coffee if he has sugar? More likely to have sugar if he has cream? Calculate these probabilities.

Guiding Questions

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Problem 2

A coin is tossed and a single six-sided number cubed is tossed. 

If landing on heads is represented by $$H$$ and landing on a $$3$$ is represented by $$R$$, determine if the following is true:

$$P(H\space\mathrm{and}\space 3)=P(H) \cdot P(3)$$

Guiding Questions

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Target Task

5-10 minutes


Today there is a 55% chance of rain, a 20% chance of lightning, and a 15% chance of lightning 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.

Next

Calculate relative frequencies in two-way tables to analyze data and determine independence.

Lesson 5
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Lesson Map

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

Topic A: Probability

Topic B: The Normal Distribution

Topic C: Statistical Inferences and Conclusions

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