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Chapter 7 · Period 1 of 10 · 50 min

Likelihood as Measurement: Introducing Probability

What is Probability? · Inquiry-based method

This unit opens the chapter by anchoring probability to a measurement analogy — students who resist abstract definitions often respond well to the idea of a scale. A common confusion at this stage is treating 'equally likely' and 'possible' as synonyms: a rainbow is possible but not equally likely alongside 'no rainbow'. Students who finish early may read the table of everyday events referenced in section 7.1 of the textbook for further anchoring examples.

0-12Open with the think-and-reflect question: a coin toss is used before a cricket match to decide who bats first — ask students why this is considered fair. Invite two or three brief responses. Draw out the idea that neither team can predict the outcome, yet both outcomes are equally possible. Record the key phrase 'equally likely' on the board.
12-30Introduce probability as a measurement of likelihood — just as length is measured in centimetres, likelihood is measured on a scale from 0 to 1. Discuss what the endpoints and midpoint mean: 0 means impossible, 1 means certain, 0.5 means an even chance. Ask students to place informal everyday events (a stone dropped always falls, a rainbow appearing tomorrow, rolling a 6 on a die) somewhere on a hand-drawn number line on the board. Introduce subjective probability — an evidence-based personal judgement before any experiment is run.
30-50Students work individually on Exercise Set 7.1 Q1, p.159: rank four events on the scale and label each with the correct band term. Pair-share answers and discuss disagreements. Close by eliciting that probability is not a guess — it is a reasoned position that will be sharpened by formal methods in later work.
Assessment

Competency (C-6.2). Applies probability to estimate and reason about the likelihood of everyday random events.

Learning outcome. Students can place everyday events on the 0-to-1 probability scale and label each with the correct likelihood band (impossible, less likely, even chance, more likely, certain).

A bag contains 5 red balls and 5 blue balls. One ball is drawn at random. Which label from the probability scale best describes the event 'the ball drawn is red'?

  • A Certain
  • B Even chance
  • C Impossible
  • D Less likely

B. Even chance

What each wrong option reveals

  • A Confuses 'certain' with any outcome that is possible; overlooks that blue balls are equally present.
  • C Confuses 'impossible' with any outcome that is not guaranteed; does not recognise that red balls are present in the bag.
  • D Correctly recognises the event is not certain, but misjudges the relative count — treats 5 out of 10 as a minority rather than an equal share.
Chapter 7 · 10 periods of 50 min

Also saved as 6 periods or 8 periods.

  • 2Randomness, Random Experiments, and the Probability Scale
    Randomness, Random Experiments, and the Probability…
  • 3Two Routes to Probability: Experimental and Theoretical
    Measuring Probability Objectively
  • 4Experimental Probability: Relative Frequency from Trials
    Experimental Probability: Performing Observations or Experiments
  • 5Theoretical Probability: Equally Likely Outcomes and P(Event) Notation
    Theoretical Probability
  • 6Statistical Data, Population Estimates, and the Gambler's Fallacy
    Analysing Statistical Data Using Probability
  • 7Sample Spaces: Listing All Possible Outcomes Completely
    Sample Space
  • 8Events as Subsets of the Sample Space
    Events
  • 9Tree Diagrams: Enumerating Multi-Step Experiment Outcomes
    Tree Diagrams
  • 10Whole-Chapter Synthesis: Choosing and Applying the Right Probability Tool
    Synthesis
Ganita Manjari · Class 9 · 14 chapters

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