Teaching mathematics

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# 4.1 Equal likelihood

‘All events are equally likely.’

When discussing how likely an event is to occur, a common misunderstanding is that all events must be equally likely. In some cases, for example when throwing a dice or tossing a coin, the outcomes are all equally likely. However, there are many instances when this is not the case.

Tim says, ‘Tomorrow it will either rain or not rain, so the probability that it will rain is 50:50.’

Figure 29 Child splashing in a puddle

## Activity 15 Reflecting

Timing: Allow 5 minutes

What is wrong with Tim’s logic in this instance?

### Discussion

Tim has identified two outcomes: rain or not rain. He has therefore deduced that the probability of rain is 0.5. While he is right that rain and not rain are mutually exclusive (i.e. cannot both occur at the same time), there are many factors involved in calculating a weather forecast. It is not usually the case that the probability of rain is exactly the same as the probability of it not raining.

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