Big Idea:

Big Idea 2

Probability calculations can be applied to solve problems and make decisions.

1 week

Evidence of Understanding​​

  • compare probabilities of different events occurring and describe their effect on each other
    • categorize and justify if/when events are mutually exclusive (when the probability of the events occurring simultaneously is 0), dependent (including both unions and intersections of sample spaces), or independent
      • analyze and relate the multiplication rule and addition rule to the sample space and relationship between events
    • show that events are independent if and only if the product of their probabilities is equal to the joint probability of the events occurring
    • articulate how one event affects a subsequent event (conditional probability) when events are independent or dependent
    • explain how the correct probability formula describes a desired operation/analysis on the sample space
       
  • use probability to predict and evaluate outcomes and expected values of decisions
    • determine which probability formula should be used to predict outcomes for a given context
    • apply probability rules to a given context and interpret the meaning of the outcomes within that context
      • (+) weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
    • calculate the expected payoff for a game of chance
      • Example: find the expected winnings from a state lottery ticket or a game at a fast-food restaurant
    • use probability and outcome values to justify the fairness of a particular system (and if necessary can make recommendations to make the system more fair)
    • evaluate and compare strategies using expected values
      • Example: compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident
    • explain whether a model is consistent with results from a data-generating process
      • Example: a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Develop conceptual understanding:

mutually exclusive, independent, dependent, multiplication rule, addition rule, conditional probability, fairness, expected value

Supporting terms to communicate:

if and only if, sample space, frequency, event space, complimentary, expected value, possible outcomes, simultaneous, union, intersection, permutation, combination, disjoint, compound
Core Resource

A core resource supports multiple days of instruction. For this Big idea, a partial Core Resource is provided as a starting place for teachers.

  • Comparing Events
    This partially constructed Core Resource is intended to support students in making connections between the sample spaces for events and the formulas that can be used to calculate the probability of those events occurring.
    Resource:
    Comparing Events

    This partially constructed Core Resource is intended to support students in making connections between the sample spaces for events and the formulas that can be used to calculate the probability of those events occurring.

    All Resources From:
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.
  • Complementary Probability
    Use the structure of a tree diagram to quickly calculate the probability an event does not occur by chunking the tree diagram into the events that match and the events that do not.
    Resource:
    Complementary Probability

    Use the structure of a tree diagram to quickly calculate the probability an event does not occur by chunking the tree diagram into the events that match and the events that do not.

    All Resources From: