1. Who is cheating?
A new test is in development to try to identify athletes who use a certain banned substance to enhance their performance.
The development team has accumulated data which indicates that although the test shows good results in detecting an athlete who has used this substance, the number of false positives is more worrying.
What are the chances an athlete will be unfairly accused, or will get away with cheating?

2. In your pairs you should have:
a die
recording grid
red, blue, green and yellow coloured pencils
Worksheet 1
Sample Space worksheet
Worksheet 2

3. How it works:
Throw one die to determine whether the athlete is doping. A 5 or 6 means they are.
If they are doping, throw two dice.
If the total is 4, it is a negative test, otherwise it is positive.
If they aren’t doping, flip a coin three times.
If you get HHH, it is a positive test, otherwise, it is negative.
Not doping
doping
Positive test
Negative test

4. Throw one die 5 or 6. Doping. 1, 2, 3 or 4. Not doping Throw two dice.
Flip a coin three times.
Total of 4.
Negative test
Total not 4.
Positive test
Anything else
Negative test
HHH
Positive test

5. What do each of these mean?
Now repeat the experiment 36 times in total and record on your sheet  
You should end up with 36 pairs of coloured blocks.

6. Throw one die 5 or 6. Doping. 1, 2, 3 or 4. Not doping Throw two dice.
Flip a coin three times.
Total of 4.
Negative test
Total not 4.
Positive test
Anything else
Negative test
HHH
Positive test

7. So what are the chances that someone will be wrongly accused?
What does the evidence on your recording sheet suggest?
Are you surprised by what you see?
Complete the tree diagram and 2-way table for the results of your experiment.

8. Fill in the Sample Space sheet to help you find what you should expect to happen.

9. What are all the possibilities when flipping a coin three times?
Try to be systematic.

10. How do the experimental results compare with what we would expect?
Complete worksheet 2