Big Idea:

Big Idea 1

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

1 week

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.
  • Experimenting With Probability
    This multiple-day resource introduces students to the big ideas of probability.
    Resource:
    Experimenting With Probability

    The goal of these resources is to activate students’ current understanding of probability and to help students make the connection between experimental and theoretical probability and to see that there is more variability for a small number of trials than for a larger number of trials.

    All Resources From:
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.