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Teaching mathematics
Teaching mathematics

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4.3 Sample space considerations

‘If events are random, the results of a series of independent events are equally likely.’

For example: if you toss a coin twice, it is equally likely that you will get heads, heads as heads, tails.

A photo of a hand flipping a coin.
Figure 31 Hand flipping coin


It is important to draw a sample space diagram for multiple events as it is not necessarily the case that all outcomes are equally likely.

Tossing a coin twice is a very good example of when this is not the case.

When one coin is tossed, the outcome is either heads (H) or tails (T), so the probability of each outcome is one divided by two.

When two coins are tossed, the first coin can be either H or T and the second coin can be either H or T. This results in the sample space: HH, HT, TH, TT.

This means that the probability of getting two heads (HH) is one divided by four and the probability of getting one head and one tail (TH or HT) is one divided by two. The two events are not equally likely.