Everyday maths for Health and Social Care and Education Support 1

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# 9 Probability

Probability is measuring how likely it is that something will happen. We use probability in different ways in real life:

• Insurance actuaries use probability to decide how much to charge for all the different types of insurance and assurance there is. For example health insurance or travel insurance to cover unexpected treatment for medical emergencies abroad.
• Government departments use probability and statistics to help them govern the country including the National Health Service and the Department for Education.
• National vaccination programmes are based on the likelihood and prevalence of certain illnesses. For example, the national tuberculosis vaccination programme was stopped in secondary schools when the chance of contracting the disease in the UK was considered to be very low risk.

(Another word for probability is chance. You might say, ‘What are the chances of this happening?’)

Working through this section will enable you to:

• understand the possibility of different events happening
• show that some events are more likely to occur than others
• understand and use probability scales
• show the probability of events happening using fractions, decimals and percentages.

Probability is measuring how likely it is that something will happen. Look at the word itself: ‘probability’. Can you see it is related to the word ‘probable’?

We know that life is full of choices and chances, or that some things are more likely to happen than others.

For example, you could say, ‘I might go to the gym tomorrow.’ Probability would be used to measure how likely it is that you will go to the gym. There are two options involved here: either you go to the gym or you don’t.

If you knew that you had lots of other things to do tomorrow (and you hate going to the gym), then the probability of actually going would be low or even zero! But on the other hand, if you really intended to go to the gym and had even booked a place in a fitness class then the probability of going to the gym would be high.

We use probability to give us an idea of how likely it is that something will happen. It gives us a measuring system.

• If something is very likely to happen, the probability is high.
• If something is not very likely to happen, the probability is low.

## Example: What are the chances?

What’s the probability of:

• you winning the lottery this week?
• catching a cold this winter?
• running a marathon this summer?

There’s a very low probability that you’ll win the lottery this week or run a marathon this summer (unless you have already been training for a marathon). For most people, the probability of catching a common cold, at some point over the winter, will be high.

Of course, some things have even chances of happening. For example, if you toss a coin, there is an equal probability of it being heads or tails. This could also be called an even chance, or a fifty-fifty chance, of the coin being heads or tails.

How many different things that have different chances of happening can you think of?

Now try the following activity. Remember to check your answers once you have completed the questions.

## Activity 14: Thinking about probability

Take a look at the table, think of some events to add to each of the columns.

Events with a high probability of happening Events with an even chance of happening Events with a low probability of happening
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There is no single correct answer to this activity. Have a look at our suggestions below:

Events with a high probability of happening Events with an even chance of happening Events with a low probability of happening
Catching a common cold during the winterTossing a coin and getting headsWinning the lottery
DeathA baby being born a boyBeing kidnapped by aliens
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