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Mathematics · Grades 6–10

Probability: what a result does and does not show

Equal counting works only when the individual outcomes are equally likely.

Make a worksheet

Understand the idea

Count the sample space

Equal counting works only when the individual outcomes are equally likely.

Long-run versus one trial

A probability is not a promise about the next result or a small number of trials.

Examples and reasoning

A fair six-sided die is rolled. What is the probability of an even number as a simplest fraction?

1/2

1/2

A fair six-sided die is rolled. What is the probability of a result greater than 4?

1/3

1/3

Check your understanding

  1. A fair coin lands heads three times. The next independent toss has head probability

    1. 1
    2. 0
    3. 1/2
    4. 3/4

  2. An event cannot happen in the defined sample space. Its probability is

    1. 2
    2. 0
    3. −1
    4. 1

  3. An event is certain in the defined sample space. Its probability is

    1. 1
    2. −1
    3. 100 as a decimal probability
    4. 0

  4. Why does counting red regions on a spinner not work if the regions have unequal angles?

Answers and marking notes

Answers and marking notes
  1. 1/2

    1/2

  2. 0

    0

  3. 1

    1

  4. Different regions may have different probabilities; their angular sizes, not just their count, matter in an ideal uniform spinner.

    Different regions may have different probabilities; their angular sizes, not just their count, matter in an ideal uniform spinner.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.