### Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

### Marbles and Bags

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

### Win or Lose?

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?

# Statins and Risk

##### Age 14 to 16Challenge Level

This resource is part of the collection Should I Risk It?

This problem follows on from How Risky is a Bacon Sandwich?

Watch the video below, where Professor David Spiegelhalter discusses the benefits and risks of taking statins.

If you cannot view the video, click below to view some alternative text.

"NEW STATIN CUTS HEART RISK FOR EVERYONE"
"Taking statins every day reduces the risk of a heart attack or stroke over the next 10 years by 40%"

This newspaper headline claims that taking statins is a good idea. Statins are drugs that reduce cholesterol, which in turn reduces the risk of a heart attack or stroke.

Do you think that Professor Spiegelhalter should be taking statins? What information would help you to make sense of this newspaper headline?

The 40% risk in the newspaper story is a relative risk reduction.

To determine whether this is important, you need to know your baseline absolute risk. This is the chance of suffering from a heart attack or stroke in the next 10 years if you do not take the drug.

Professor Spiegelhalter has found out that people like him (age, blood pressure, lifestyle factors) have a baseline absolute risk of about 10%.

How can this information help Professor Spiegelhalter assess the benefit of him taking statins?

Do you agree with his analysis in the video below?

The 10% risk could be reduced by 40% if Professor Spiegelhalter took statins every day.

If there were 100 people like Professor Spiegelhalter, then we would expect 10 of them to have a heart attack or stroke in the next 10 years.

If they all took statins every day, then this number would be reduced by 40%. This means that only 6 of the 100 would have a heart attack or stroke in the next 10 years.

This means statins prevent a heart attack or stroke for $\tfrac{4}{100}$ or $\tfrac{1}{25}$ of the population. The other $\tfrac{24}{25}$ would gain no benefit.

What other factors might affect Professor Spiegelhalter's decision whether to take the drug?

What decision would you make in his position?
Look at the video below to see if you have made the same choice as he has.

Professor Spiegelhalter can't decide whether or not he should take the drug!
Although the drug provides some benefits, it also has some side effects.

The calculation provides the evidence that allows you to make an informed decision, but it doesn't determine what you should do. Each person has to decide for themselves whether the potential benefits to them outweigh the side effects.

Below are some more newspaper headlines. What other information would you need to evaluate the risks mentioned?

Statins Linked to Raised Risk of Type 2 Diabetes
Taking statins increases the risk of getting type 2 diabetes over the next 2 years by 50%.

Ibuprofen can raise risk of heart attack
People prescribed ibuprofen were 24% more likely to suffer from a heart attack in the next three months.

An aspirin a day could double cancer survival rates
Aspirin increases 5-year cancer survival rates by 80%.

For another activity examining newspaper headlines and risk, try Trusting the Tabloids.

Understanding Uncertainty, Professor Spiegelhalter's website, has lots of articles about probability and risk that you might find interesting. There are some suggestions below, but there's lots more you can explore.