Probability and Statistical Inference

Lesson 6

Math

Unit 8

11th Grade

Lesson 6 of 13

Objective


Use conditional probability to make decisions about medical testing.

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.

Criteria for Success


  1. Describe that no test for identifying a disease is perfect and that there are times when a test records a positive result when there is not disease present and that there are times when a test records a negative result when there is a disease present. 
  2. Identify conditional probabilities in medical testing scenarios. 
  3. Use multiple representations to visualize a probability situation with medical testing and use these representations to determine probabilities. 
  4. Model situations by calculating probabilities from given sample sizes and associated data.
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Anchor Problems

25-30 minutes


Problem 1

Which tree diagram corresponds with which table? How do you know?

Guiding Questions

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References

New Visions for Public Schools Matching Two Way Frequency Tables and Tree Diagrams

Matching Two Way Frequency Tables and Tree Diagrams is made available by New Visions for Public Schools under the CC BY-NC-SA 4.0 license. © 2017 New Visions for Public Schools. Accessed https://curriculum.newvisions.org/math/resources/resource/algebra-ii-unit-5-big-idea-2-matching-two-way-frequency-tables-and-tree-diagrams/.

Modified by Fishtank Learning, Inc.

Problem 2

In a certain population, 30% of people get a particular disease. A test was developed to determine if any given person has the disease, but it isn’t perfect.

The test has a 90% chance of accurately predicting that someone has a disease, BUT it also has a 5% chance of predicting someone has this disease who doesn’t. 

Below are two models you can use to visualize this situation. 

Using the information from the problem, write in the number of people in a random sample of 2,000 who take the test for the disease and get results that are true positive, false positive, true negative, and false negative.

Guiding Questions

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Target Task

5-10 minutes


A certain test for mononucleosis has a 99% chance of correctly diagnosing a patient with mononucleosis and a 5% chance of misdiagnosing a patient who does not have the infection. Suppose the test is given where 1% of the people have mononucleosis. If a randomly selected patient’s test result is positive, what is the probability that she has mononucleosis? Explain. 

References

Illustrative Mathematics False Positive Test Results

False Positive Test Results, accessed on June 15, 2017, 9:22 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

Describe the center, shape, and spread of distributions by reasoning visually about the mean, standard deviation, and shape of a histogram.

Lesson 7
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Lesson Map

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Topic A: Probability

Topic B: The Normal Distribution

Topic C: Statistical Inferences and Conclusions

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