Probability

Lesson 5

Math

Unit 8

10th Grade

Lesson 5 of 10

Objective


Describe conditional probability and develop the rule $$P(B|A)=\frac{P(A \space \mathrm{and} \space B)}{P(A)}$$.

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.5

Criteria for Success


  1. Describe conditional probability as the probability of a subsequent event occurring if you already know what has been chosen as the primary event. 
  2. Use the notation $$P(B|A)$$ to represent conditional probability.
  3. Develop the rule $$ P(B│A)=\frac{P(A \space and \space B)}{P(A)}$$ for calculating the conditional probability.
  4. Describe why the formula for calculating conditional probability makes sense. 

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Anchor Problems

25-30 minutes


Problem 1

There are four red envelopes, four blue envelopes, and four $1 bills, which will be placed in four of the eight envelopes. Suppose one $1 bill is placed in a blue envelope and the three remaining $1 bills are placed in three red envelopes. 

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

Below is a tree diagram you can use to answer the questions. Write in the probabilities as described above.

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 envelopes. Record the probabilities on the tree diagram. 

  1. What is the probability, if you choose a blue envelope, that you will get the $1?
  2. What is the probability, if you choose a red envelope, 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 3

Data gathered on the shopping patterns during the months of April and May of high school students from Peanut Valley revealed the following. 38% of students purchased a new pair of shorts (call this event $$H$$), 15% of students purchased a new pair of sunglasses (call this event $$G$$), and 6% of students purchased both a pair of shorts and a pair of sunglasses. Find the probability that a student purchased a pair of sunglasses given that you know they purchased a pair of shorts. 

Guiding Questions

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References

Mathematics Vision Project: Geometry Module 8: ProbabilityLesson 6 "Go" (p. 28, #9)

Module 8: Probability from Geometry: A Learning Cycle Approach made available by Mathematics Vision Project under the CC BY 4.0 license. © 2016 Mathematics Vision Project. Accessed Sept. 20, 2018, 10:11 a.m..

Target Task

5-10 minutes


Create a situation where $$P(A|B) = P(A)$$.

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.

  • Use any of the previous Anchor Problem examples to create conditional probability problems.

Next

Determine whether events are independent.

Lesson 6
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Lesson Map

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

Topic A: Conditional Probability and the Rules of Probability

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