##### Stage: 3, 4 and 5

This resource is part of the collection Probability and Evidence.

There are often headlines in the news that seem surprising or worrying. Take a look at the headline below:

These might seem to be concerning if you like horse-riding. But what does the evidence actually tell us? How dangerous is horse riding? Look below to see how the data compares for this headline:

“Hang-gliding is safer than horse-riding … to judge by a new survey of sports deaths.”
The Times, 12 March 1987

The data:
In 1985, 15 people died in horse riding accidents, compared to one death from hang-gliding.

What else might you need to know in order to make a judgement?

We don't know from this data how many people hang-glide compared to the number who ride horses. If many more people ride horses than go hang-gliding, there may well be more deaths from horse riding despite hang-gliding being the more dangerous activity.

### Micromorts

One method we can use to compare the risks of different activities is to use a common "currency" or unit of risk.

1 micromort is defined as a 1 in a million chance of dying.
1 million micromorts is a mort, and means certain death.

For example, 1 micromort is equivalent to:
• 230 miles in a car
• 6000 miles in a train
• 3 flights
5 micromorts is equivalent to:
• A general anaesthetic in a UK hospital
• Riding a motorcycle 30 miles
• One scuba dive
• 4 hours in the life of a heroin user
• Serving for 4 hours in the UK army in Afghanistan.

Roughly what is the risk of serving in Afghanistan for one day?
What other activities could you carry out for the same risk?

To work this out you have probably assumed that it is alright to add micromorts. Read on to find out when it's OK to do this.

Suppose you travel 230 miles in a car, then 6000 miles by train. Both of these are activities that carry a risk of 1 micromort. Then, you might assume that the risk of doing both is 2 micromorts, as you add them together. However, you have to be careful when doing this.

To see where things can go wrong, imagine an alternative activity that carried a risk of 500 000 micromorts, or a $\frac{1}{2}$ chance of death.

Suppose you did this activity twice. If you added the micromort values, you would end up with a risk of 1 000 000 micromorts, or 1 mort, which would mean certain death.

However, you have a $\frac{1}{2}$ chance of survival each time, so your chances of surviving both times are $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$. This means the probability of death is $\frac{3}{4}$, which equates to 750 000 micromorts.

This is very different to adding the micromort values, which shows that we can't always add micromorts.

What is the risk of an activity of risk $a$ micromorts followed by one of risk $b$ micromorts?

Suppose that there are two activities, with risks of $a$ and $b$ micromorts associated. Then, the probability of surviving the first is $1-\frac{a}{1,000,000}$, and the probability of surviving the second is $1-\frac{b}{1,000,000}$. This means the probability of surviving both is:$$\left(1-\frac{a}{1,000,000}\right) \times \left( 1-\frac{b}{1,000,000} \right) \\ = 1-\frac{a}{1,000,000}-\frac{b}{1,000,000}+\frac{ab}{1,000,000,000,000}$$
This means the risk in micromorts is:$$a+b-\frac{ab}{1,000,000}$$

When do you think that it would be OK to ignore the final term and just treat the risk as $a+b$ micromorts?

It is only sensible to do this when the value $ab$ is much less than 1 000 000, so that this term does not make much difference to the risk. This will generally happen when $a$ and $b$ are small.

### Micromorts, Horse-Riding and Hang-Gliding

This interactivity, on the Understanding Uncertainty website, allows you to explore the risks of different activities in terms of the number of micromorts.

Alternatively, click on the button below to show the relevant information:

One hang-gliding flight is equivalent to 8 micromorts.

One ride on a horse is equivalent to half a micromort.

Which of horse-riding and hang-gliding do you now think is the most dangerous?

What do you make of the headline now?

If you are interested, you can find out more about risks and micromorts by reading this Plus article.