Curriculum / Math / 11th Grade / Unit 8: Probability and Statistical Inference / Lesson 4
Math
Unit 8
11th Grade
Lesson 4 of 13
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Determine when events are independent and describe independent events using everday language.
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.
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 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
The blog post, Teaching Probability Day 7 - Conditional Probability by Slightly Skewed uses LearnZillion and is useful context.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Back to the diner!
You want to know if choosing cream or sugar are independent events, that is, if one depends on the other.
Below is a Venn diagram that represents the number of people in the diner one morning. A random person is chosen. Is this random person more likely to have cream in his coffee if he has sugar? More likely to have sugar if he has cream? Calculate these probabilities.
A coin is tossed and a single six-sided number cubed is tossed.
If landing on heads is represented by $$H$$ and landing on a $$3$$ is represented by $$R$$, determine if the following is true:
$$P(H\space\mathrm{and}\space 3)=P(H) \cdot P(3)$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Today there is a 55% chance of rain, a 20% chance of lightning, and a 15% chance of lightning and rain together. Are the two events “rain today” and “lightning today” independent events? Justify your answer.
Rain and Lightning., accessed on June 15, 2017, 8:52 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 3
Lesson 5
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
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
Use conditional probability to make decisions about medical testing.
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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