9.1 Probability scales

In real life, things usually fall somewhere in between the two extremes of ‘will never happen’ and ‘will definitely happen’.

We can use a probability scale to measure how likely events are to occur:

Figure 13 A probability scale

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An illustration of a probability scale. It is a horizontal line: above the line, the left-hand end is labelled ‘Impossible’ and the right-hand end is labelled ‘Certain’; below the line, the left-hand end is labelled ‘0’, the midway point is labelled ‘’ and the right-hand end is labelled ‘1’.

Figure 13 A probability scale

• The probability of an impossible event (‘will never happen’) is 0.
• The probability of a certain event (‘will definitely happen’) is 1.
• All other events come between 0 and 1.
• Events with an even chance have a probability of .

Now try the following activity, where you’ll need a ruler and a pencil. Remember to check your answers once you have completed the questions.

Activity 15: Looking at probability

Use a ruler to draw your own probability scale. Mark on it 0, 1/2 and 1. Label 0 as ‘impossible’ and 1 as ‘certain’.

Then mark these statements on the probability scale with crosses and label them with their question letter:

• a.The probability that the sun will rise tomorrow.
• b.The probability that you will run the London Marathon next year.
• c.The probability of dying one day.

Answer

Here are the answers:

Figure 14 A probability scale (answer)

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An illustration of a probability scale. It is a horizontal line: above the line, the left-hand end is labelled ‘Impossible’ and the right-hand end is labelled ‘Certain’; below the line, the left-hand end is labelled ‘0’, the midway point is labelled ‘’ and the right-hand end is labelled ‘1’. A cross labelled ‘(b)’ is about a quarter of the way along the line; a second cross, labelled ‘(a)’ and ‘(c)’, is at the right-hand end of the line.

Figure 14 A probability scale (answer)

Of course, if you are a long-distance runner or plan to be one, your location for (b) might be closer to 1!