Curriculum / Math / 10th Grade / Unit 8: Probability / Lesson 2
Math
Unit 8
10th Grade
Lesson 2 of 10
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Determine the probability of events with replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
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.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.B.6 — Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
S.CP.B.7 — Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
7.SP.C.7 — Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
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.
7.SP.C.6 — Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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
Below is a spinner with four quadrants, each labeled 1 through 4. Each outcome is equally likely.
Sam spins the spinner twice and doesn't land on 4. What is the probability of this occuring?
Dan has shuffled a deck of cards. He chooses a first card, looks at it, puts the card back into the deck, shuffles again, and finally chooses a second card. What is the probability that Dan’s two cards are of the same suit?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Use the game scenario to answer the following questions.
Game Tools: Spinner 1 (three equal sectors with the number 1 in one sector, the number 2 in the second sector, and the number 3 in the third sector) Card bag (Blue-A, Blue-B, Blue-C, Blue-D, Red-E, Red-F)
Directions: Spin Spinner 1 and randomly select a card from the card bag (four blue cards and two red cards). Record the number from your spin and the color of the card selected.
Algebra II > Module 4 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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 1
Lesson 3
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
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
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.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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