Curriculum / Math / 10th Grade / Unit 8: Probability / Lesson 5
Math
Unit 8
10th Grade
Lesson 5 of 10
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Describe conditional probability and develop the rule $$P(B|A)=\frac{P(A \space \mathrm{and} \space B)}{P(A)}$$.
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.5 — Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
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
There are four red envelopes, four blue envelopes, and four $1 bills, which will be placed in four of the eight envelopes. Suppose one $1 bill is placed in a blue envelope and the three remaining $1 bills are placed in three red envelopes.
Below is a tree diagram you can use to answer the questions. Write in the probabilities as described above.
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 envelopes. Record the probabilities on the tree diagram.
Data gathered on the shopping patterns during the months of April and May of high school students from Peanut Valley revealed the following. 38% of students purchased a new pair of shorts (call this event $$H$$), 15% of students purchased a new pair of sunglasses (call this event $$G$$), and 6% of students purchased both a pair of shorts and a pair of sunglasses. Find the probability that a student purchased a pair of sunglasses given that you know they purchased a pair of shorts.
Module 8: Probability from Geometry: A Learning Cycle Approach made available by Mathematics Vision Project under the CC BY 4.0 license. © 2016 Mathematics Vision Project. Accessed Sept. 20, 2018, 10:11 a.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Create a situation where $$P(A|B) = P(A)$$.
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 4
Lesson 6
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.
7.SP.C.8 S.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.7 S.CP.A.2 S.CP.A.4 S.CP.B.6 S.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.7 S.CP.A.2 S.CP.B.6 S.CP.B.7 S.CP.B.8
Determine the probability of events that are not mutually exclusive to formalize the addition rule.
S.CP.A.1 S.CP.A.2 S.CP.B.7
S.CP.A.3
Determine whether events are independent.
S.CP.A.2 S.CP.A.3 S.CP.A.5
Calculate and analyze relative frequencies in two-way tables to make statements about the data and determine independence.
S.CP.A.4 S.CP.A.5 S.ID.B.5
Make decisions about medical testing based on conditional probabilities.
S.CP.A.3 S.CP.A.4 S.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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