Curriculum / Math / 10th Grade / Unit 8: Probability / Lesson 8
Math
Unit 8
10th Grade
Lesson 8 of 10
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Lesson Notes
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Make decisions about medical testing based on conditional probabilities.
The core standards covered in this lesson
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.4 — Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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In terms of pacing, this lesson should spread over two days due to the depth of this content.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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 the disease who doesn’t —a false positive. Find the number of people in a random sample of 2,000 people who take the test for the disease who get results that are true positive, false positive, true negative, and false negative in the two-way table and tree diagram below.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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 they have mononucleosis? Explain.
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.
Next
Describe and apply the counting principle and permutations to contextual and non-contextual situations.
Topic A: Conditional Probability and the Rules of Probability
Describe the sample space of an experiment or situation. Use probability notation to identify the “and,” “or,” and complement outcomes from a given sample space.
Standards
7.SP.C.8S.CP.A.1
Determine the probability of events with replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
7.SP.C.7S.CP.A.2S.CP.A.4S.CP.B.6S.CP.B.7
Determine the probability of events without replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
7.SP.C.7S.CP.A.2S.CP.B.6S.CP.B.7S.CP.B.8
Determine the probability of events that are not mutually exclusive to formalize the addition rule.
S.CP.A.1S.CP.A.2S.CP.B.7
Describe conditional probability and develop the rule $$P(B|A)=\frac{P(A \space \mathrm{and} \space B)}{P(A)}$$.
S.CP.A.3
Determine whether events are independent.
S.CP.A.2S.CP.A.3S.CP.A.5
Calculate and analyze relative frequencies in two-way tables to make statements about the data and determine independence.
S.CP.A.4S.CP.A.5S.ID.B.5
S.CP.A.3S.CP.A.4S.CP.A.5
S.CP.B.9
Describe and apply the counting principle and combinations to contextual and non-contextual situations.
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