Probability and Statistical Inference

Lesson 3

Math

Unit 8

11th Grade

Lesson 3 of 13

Objective


Calculate conditional probabilities.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 7.SP.C.8

Criteria for Success


  1. Describe conditional probability as the probability of one event occurring given knowledge of a different event. 
  2. Use the notation $${P(B|A)}$$ to represent conditional probabilities.
  3. Develop the rule $${P(B|A)}={P(A \space\mathrm{and}\space B)\over{P(A)}}$$.

Tips for Teachers


  • The Khan Academy video, "Conditional probability explained visually" describes the idea of conditional probability really well.
  • If students are stuck on the idea of each part of the tree diagram being a one outcome, you can have them take an initial step of writing the “$1” and “no $1” the number of times that it is actually represented in each of the color envelopes. 
  • Anchor Problem #2 is an introduction to developing the conceptual understanding for testing independence of events. 
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Anchor Problems


Problem 1

There are four red envelopes, four blue envelopes, and four $1 bills, which will be placed in four of the eight envelopes.

Below is a tree diagram we can use to answer the questions that follow. Write in the probabilities described. 

Suppose one $1 bill is placed in a blue envelope, and the three remaining $1 bills are placed in three red envelopes.

If you choose a blue envelope, what is the probability that you will get the $1? 

If you choose a red envelope, what is the probability that you will get the $1?

Guiding Questions

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References

Illustrative Mathematics Lucky Envelopes

Lucky Envelopes, accessed on June 15, 2017, 8:49 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.

Modified by Fishtank Learning, Inc.

Problem 2

Suppose the $1 bills are redistributed among the envelopes. Two $1 bills are placed in two blue envelopes, and two $1 bills are placed in two red envelops. Record the probabilities on the tree diagram.

If you choose a blue envelope, what is the probability that you will get the $1? 
If you choose a red envelope, what is the probability that you will get the $1? 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Lucky Envelopes

Lucky Envelopes, accessed on June 15, 2017, 8:49 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.

Modified by Fishtank Learning, Inc.

Target Task


You flip a coin twice. $${P(A)}$$ is the probability of heads on the first flip, and $${P(B)}$$ is the probability of heads on the second flip. Describe why, in this situation, $$P(A|B)={P(A)}$$.

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Lesson 2

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Lesson 4

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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