Curriculum / Math / 11th Grade / Unit 8: Probability and Statistical Inference / Lesson 6
Math
Unit 8
11th Grade
Lesson 6 of 13
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Use conditional probability to make decisions about medical testing.
The core standards covered in this lesson
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Which tree diagram corresponds with which table? How do you know?
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/.
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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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.Â
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.
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.
Lesson 5
Lesson 7
Topic A: Probability
Determine probabilities of mutually exclusive events.
S.CP.A.1
Determine probabilities of events that are not mutually exclusive.
S.CP.A.1 S.CP.B.6 S.CP.B.7
Calculate conditional probabilities.
S.CP.A.3
Determine when events are independent and describe independent events using everday language.
S.CP.A.2 S.CP.A.3 S.CP.A.5
Calculate relative frequencies in two-way tables to analyze data and determine independence.
S.CP.A.4
S.CP.A.2 S.CP.A.3
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Topic B: The Normal Distribution
Describe the center, shape, and spread of distributions by reasoning visually about the mean, standard deviation, and shape of a histogram.
S.IC.A.1
Derive and calculate population percentages based on a normal distribution of data.
S.IC.A.2 S.IC.B.4
Use $${z-}$$scores to identify population percentiles.
S.IC.B.4
Topic C: Statistical Inferences and Conclusions
Describe and compare statistical study methods.
S.IC.B.3 S.IC.B.6
Use multiple random samples to estimate a population mean or proportion and verify the validity of the sampling method by analyzing the means and standard errors of samples.
Calculate and describe the margin of error in context and use larger sample sizes to minimize the margin of error.
Compare two treatments in experimental data and determine if the difference between the two treatments is significant.
S.IC.B.5
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