Curriculum / Math / 11th Grade / Unit 8: Probability and Statistical Inference / Lesson 3
Math
Unit 8
11th Grade
Lesson 3 of 13
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Lesson Notes
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Calculate 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.
The foundational standards covered in this lesson
7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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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
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?
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.
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?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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, $$P(A|B)={P(A)}$$.
Next
Determine when events are independent and describe independent events using everday language.
Topic A: Probability
Determine probabilities of mutually exclusive events.
Standards
S.CP.A.1
Determine probabilities of events that are not mutually exclusive.
S.CP.A.1S.CP.B.6S.CP.B.7
S.CP.A.3
S.CP.A.2S.CP.A.3S.CP.A.5
Calculate relative frequencies in two-way tables to analyze data and determine independence.
S.CP.A.4
Use conditional probability to make decisions about medical testing.
S.CP.A.2S.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.2S.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.3S.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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