Curriculum / Math / 10th Grade / Unit 8: Probability / Lesson 6
Math
Unit 8
10th Grade
Lesson 6 of 10
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Lesson Notes
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Determine whether events are independent.
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 essential concepts students need to demonstrate or understand to achieve the lesson objective
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
25-30 minutes
You are in a diner and 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.
A coin is tossed and a single six-sided die is rolled. If landing on heads is represented by $$H$$ and rolling a $$3$$ is represented by $$R$$, determine if the following is true:
$$P(H \space and \space 3)=P(H)\cdot P(3)$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Today there is a 55% chance of rain, a 20% chance of lightning, and a 15% chance of lighting 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.
Next
Calculate and analyze relative frequencies in two-way tables to make statements about the data and determine independence.
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
S.CP.A.2S.CP.A.3S.CP.A.5
S.CP.A.4S.CP.A.5S.ID.B.5
Make decisions about medical testing based on conditional probabilities.
S.CP.A.3S.CP.A.4S.CP.A.5
Describe and apply the counting principle and permutations to contextual and non-contextual situations.
S.CP.B.9
Describe and apply the counting principle and combinations to contextual and non-contextual situations.
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