Understand the Basic Nature of Probability
Course No. / 27.09720 / Course Name / GSE Analytic Geometry
Grade / 10 / Unit # / 7 / Projected
Timeline / 3 weeks
Unit Name / Applications of Probability
Unit Overview
In this unit, students will:
• take their previously acquired knowledge of probability for simple and compound events and expand that to include conditional probabilities (events that depend upon and interact with other events) and independence
• be exposed to elementary set theory and notation (sets, subsets, intersection and unions)
• use their knowledge of conditional probability and independence to make determinations on whether or not certain variables are independent
Unit Curriculum Map
Unit Standards / MGSE9-12.S.CP.1Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).
MGSE9-12.S.CP.2Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.
MGSE9-12.S.CP.3Understand the conditional probability of A given B as P(A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is, 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.
MGSE9-12.S.CP.4Construct 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, use collected 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.
MGSE9-12.S.CP.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.
MGSE9-12.S.CP.6Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in context.
MGSE9-12.S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answers in context.
Content Learning Progression # _1___
Topic _1__ out of _2__ / Probability (1 week)
Standards in this learning progression: / MGSE9-12.S.CP.1
MGSE9-12.S.CP.2
Connections to other standards (Standards for Mathematical Practice, Literacy, etc: / 1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Resource 1:
Resource 2:
Terms students should learn and use with precision in this unit and progression: / complement (complement of B is or , dependent events, element, experimental probability, independent events, intersection of sets , multiplication rule for independent events , mutually exclusive, null set, outcome, overlapping events, sample space, set, set notation, subset, theoretical probability, union of sets , Venn diagram
Materials and tools students should use with precision in this unit and progression: / Dice or number cubes, coins, cards, spinners, calculator, simulation program on calculator or computer
Know – Understand – Do
(KUD)
By the end of this learning progression, students will be able to…
UNDERSTAND
Big Ideas, Essential Understandings, or Generalizations
Independence of events.
How to interpret data using the probability of an event.
KNOW
Facts and Procedural Knowledge / DO
Skills
- Understand the basic nature of probability
- Know how to use Venn Diagrams to represent the interactions between different sets, events or probabilities
- Know how to use a two-way frequency table
- Know how to analyze games of chance, business decisions, public health issues and a variety of other parts of everyday life can be probability
- Represent set notation to algebraic represent complex networks of events or real world objects
- Represent everyday occurrences mathematically through the use of unions, intersections, complements and their sets and subsets
- Determine probabilities of simple and compound events
- Organize and model situations involving probability
- Read and understand frequency tables
Content Learning Progression # _2___
Topic _2__ out of _2__ / Conditional Probability
(2 weeks)
Standards in this learning progression: / MGSE9-12.S.CP.3
MGSE9-12.S.CP.4
MGSE9-12.S.CP.5
MGSE9-12.S.CP.6
MGSE9-12.S.CP.7
Connections to other standards (Standards for Mathematical Practice, Literacy, etc: / 1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Resource 1:
Resource 2:
Terms students should learn and use with precision in this unit and progression: / Addition rule ,
conditional probability
(GaDOE Formula Sheet: )
Materials and tools students should use with precision in this unit and progression: / Dice or number cubes, coins, cards, spinners, calculator, simulation program on calculator or computer
Know – Understand – Do
(KUD)
By the end of this learning progression, students will be able to…
UNDERSTAND
Big Ideas, Essential Understandings, or Generalizations
The rules of probability to compute probabilities of compound events.
KNOW
Facts and Procedural Knowledge / DO
Skills
- Know how to recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
- Understand independence as conditional probabilities where the conditions are irrelevant
- Know how to 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.
- Know how to 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
- Explain the concepts of conditional probability
- Find the conditional probability
- Apply the Addition Rule and interpret the answer in terms of the model.
- Model situations involving conditional probability with two – way frequency tables and/or Venn Diagram