Probability

7 Components
Initial Task
Flora, Freddy, and the Future
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Medical Testing
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 5 Find aligned Regents questions with Quiz Banker End of Unit Assessment Teacher Resources ALG II Unit 5
A2 U5: Probability
Browse Components
Initial Task
Flora, Freddy, and the Future
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Medical Testing
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 5 Find aligned Regents questions with Quiz Banker End of Unit Assessment Teacher Resources ALG II Unit 5
Big Idea:

Big Idea 1

The accuracy of a prediction of a random event increases with the number of events considered.

1 week
See Standards
Common Core: Supporting Standards:
N-Q.A.2

Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling.

S-CP.B.6

Use the rules of probability to compute probabilities of compound events in a uniform probability model. 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

Use the rules of probability to compute probabilities of compound events in a uniform probability model. 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.

Common Core: Additional Standards:
S-CP.A.1

Understand independence and conditional probability and use them to interpret data. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

S-CP.A.2

Understand independence and conditional probability and use them to interpret data. 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 independence and conditional probability and use them to interpret data. 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.4

Understand independence and conditional probability and use them to interpret data. 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.A.5

Understand independence and conditional probability and use them to interpret data. 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.

Common Core: Plus Standards:
S-MD.A.2(+)

Calculate expected values and use them to solve problems. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

S-MD.A.3(+)

Calculate expected values and use them to solve problems. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.

S-CP.B.8(+)

Use the rules of probability to compute probabilities of compound events in a uniform probability model. 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.

Evidence of Understanding

  • explain how the number of trials impacts the accuracy of a prediction
    • calculate and analyze the experimental probability of an event
      • as the number of trials increases, compare the ratio of the number of times an event occurred to the number of trials
    • explain how the number of trials affects the relationship between experimental and theoretical probability (i.e. as trials increase, the value of the experimental probability approaches the theoretical probability)
    • use experimental sample space and theoretical probability to define the expected frequency of an event occurring
      • Example: If an event occurs ½ of the time, then the expected frequency of an event over 100 trials is 50
  • analyze relationships between quantities for event spaces and sample spaces within a context
    • identify quantities and describe the relationships between quantities
    • describe the sample space and event space for a particular event
    • create and justify a representation for a sample space (list of ordered pairs, a tree diagram, two way frequency tables, Venn diagrams, etc.)
      • compare relative strengths and weaknesses for each type of representation (tree diagram, two way frequency table, list of events, Venn diagram, etc)
  • compare experimental and theoretical probabilities
    • explain why the probability of an outcome must lie between 0 and 1
      • the minimum proportion of size of the event space to the sample space, corresponding to an impossible event, is 0
      • the maximum proportion of size of the event space to the sample space, corresponding to a certain event, is 1
    • justify that the sum of the probability of all possible, mutually exclusive, events occurring is 1
      • If two events A and B are complementary then the p(A) = 1 - p(B)
    • make connections between event space, sample space, number of trials, experimental and theoretical probabilities
    • predict how the number of trials impacts how closely the experimental probability matches the theoretical probability
      • Example: if an experiment is performed an infinite number of times, the results of the experiment will exactly match the theoretical probability calculated for the experiment
      • optional: consider how many trials of an experiment are reasonable to accurately estimate the probability of an event occurring
    • use the theoretical probability of an event to calculate its expected value
      • Ex: If rolling an even number on the sum of two dice is worth $12 when it comes up, then the expected value of any roll given the probability of an even number is 18/36 × $12 = $6

*Note: In this unit, there is no reason to require students to reduce fractions since doing so can potentially make seeing the connection between probability and the sample space harder to see.

Develop conceptual understanding:

trials, accuracy, prediction, experimental probability, theoretical probability, sample space, frequency, event space, mutually exclusive, complementary, expected value

Supporting terms to communicate:

probability, outcome, Tree Diagram, Two Way Frequency Table, Venn Diagram

Core Resource
A core resource supports multiple days of instruction.
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.