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Probability: theoretical probabilities

Probability: theoretical probabilities

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Why this why now

Further to developing the basic ideas and foundations of probability, we move towards more abstract measures of likelihood using calculations to assign numerical values to probability. We then revisit the visual models of probability established in the previous unit through the lens of representing and utilising theoretical probability.

Prior knowledge requirements

  • Define probability as a ratio between favourable and possible outcomes
  • Represent events using lists, tables or diagrams
  • Calculate probabilities of single and combined events

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Why this why now

Further to developing the basic ideas and foundations of probability, we move towards more abstract measures of likelihood using calculations to assign numerical values to probability. We then revisit the visual models of probability established in the previous unit through the lens of representing and utilising theoretical probability.

Prior knowledge requirements

  • Define probability as a ratio between favourable and possible outcomes
  • Represent events using lists, tables or diagrams
  • Calculate probabilities of single and combined events

Probability: theoretical probabilities

In this unit we build upon the concept of likelihood to work more mathematically with more measurable probability using fraction and decimal representations to both interpret and calculate. We revisit and develop ways to represent and compare probabilities.

13 lessons in unit

  1. 1

    Checking listing possible outcomes

    I can systematically list all the possible outcomes for one or more events.
  2. 2

    The probability scale

    I can assign a numerical value to an outcome to give the probability that the outcome will occur.
  3. 3

    Calculating theoretical probabilities from lists (one event)

    I can find theoretical probabilities from a list of possible outcomes for one event.
  4. 4

    Calculating theoretical probabilities from a table (one event)

    I can find theoretical probabilities from a table showing the possible outcomes for one event.
  5. 5

    Calculating theoretical probabilities from probability tree diagrams (one event)

    I can find theoretical probabilities from a probability tree diagram showing the possible outcomes for one event.
  6. 6

    Calculating theoretical probabilities from Venn diagrams (one event)

    I can find theoretical probabilities from a Venn diagram showing the possible outcomes for one event.
  7. 7

    Comparing multiple representations to calculate theoretical probabilities

    I can compare and contrast the usefulness of the different representations when calculating theoretical probabilities.
  8. 8

    Summing probabilities

    I can show that the probabilities of all possible unique outcomes for a trial, sum to one.
  9. 9

    Calculating theoretical probabilities from two-way tables (two events)

    I can calculate and use theoretical probabilities for combined events using two-way tables (2 events).
  10. 10

    Calculating theoretical probabilities from Venn diagrams (two events)

    I can calculate and use theoretical probabilities for combined events using Venn diagrams (2 events).
  11. 11

    Calculating theoretical probabilities from probability trees (two events)

    I can calculate and use theoretical probabilities for combined events using probability trees (2 events).
  12. 12

    Comparing multiple representations to calculate theoretical probabilities for combined events

    I can compare and contrast the usefulness of the different representations when calculating theoretical probabilities for combined events.
  13. 13

    Problem solving with theoretical probability

    I can use my knowledge of probability to solve problems.

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