The Dog Ate My Homework!

A certain teacher, Mr L I Detector, claims he can tell when students are lying about their homework.

This is true.

Unfortunately, he also accuses some students who are telling the truth.

So what are the chances that someone will be wrongly accused?

You are going to investigate this question through a practical experiment.
Start by collecting a 6-sided die, and some red, blue, green and yellow multi-link cubes.

First investigate what happens for one student:

Throw the die.
- If you get a 6, this means the student is lying about their homework. Take a red cube.
- If you get any other result, the student is telling the truth. Take a blue cube.
If you got a 6, you don't need to throw the die again (why not?). Take a yellow cube - this indicates that Mr D accuses the student of lying about their homework.
If you didn't get a 6, throw the die again.
- A 1 means that Mr D accuses the student, even though they were telling the truth. Take a yellow cube.
- Anything else means that Mr D believes the student. Take a green cube.

Put your two cubes together.

What do each of these mean?

red and yellow
blue and yellow
blue and green

Why can't you have red and green?

Now repeat the experiment 36 times in total. You should end up with 36 pairs of cubes.

Are you surprised by your results?

How do they compare with what you would expect? (You may find this worksheet helpful here).

What proportion of truthful students are accused? So what is the probability of a truthful student being accused? Are you surprised by this?

Is the probability that a truthful student is accused the same as the probability that an accused student is actually telling the truth?