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### Number and algebra

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# Probability and Evidence

The problems in this collection are about thinking about which questions to ask, and how to interpret the answers.

For example, almost everyone who gets measles gets spots. If you go to your doctor with spots, they won't conclude that you're very likely to have measles, as there are many other diseases that can cause spots.

You need to be careful about the difference between the probability of getting spots if you have measles and the probability of having measles if you get spots. This mistake has caused numerous misunderstandings in medicine, law and wider society.
### Spots and Measles

### Evidence and Headlines

### Probability in Court

### Do Rare Events Happen?

### Matching Criminals

### The ELISA Test

*These resources were originally developed by the Millennium Mathematics Project Motivate Programme in collaboration with Professor Philip Dawid, funded by a Wellcome Trust grant.*

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*This collection of resources was developed in collaboration with Professor Philip Dawid of the University of Cambridge*

The problems in this collection are about thinking about which questions to ask, and how to interpret the answers.

For example, almost everyone who gets measles gets spots. If you go to your doctor with spots, they won't conclude that you're very likely to have measles, as there are many other diseases that can cause spots.

You need to be careful about the difference between the probability of getting spots if you have measles and the probability of having measles if you get spots. This mistake has caused numerous misunderstandings in medicine, law and wider society.

Age 11 to 16

Challenge Level

99% of people who have measles have spots. Ben has spots. Do you think he has measles?

Age 11 to 18

Headlines sometimes distort the truth. Read about how micromorts can be used to compare the risks of different activities.

Age 14 to 18

Challenge Level

When you're on trial for murder, it can be crucial that the court understands probability...

Age 11 to 16

Challenge Level

I'd be very surprised if I had three children all with the same birthday, but I read in the paper that it happened to one family...

Age 14 to 18

Challenge Level

DNA profiling is an invaluable tool for the police. However, when it comes to probability, things aren't always as straightforward as they seem.

Age 14 to 18

Challenge Level

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?