Introducing the problem
We are going to use a task to model an alternative approach to teaching problems involving conditional probability.
In this step, we will present the task and give you an opportunity to make sense of the questions posed. We do not expect you to attempt to answer the questions now: in subsequent steps we will be looking at several ways in which this kind of problem can be tackled.
Here is the problem:
A certain teacher, Mr L I Detector, claims that he can tell when students are lying when they make an excuse about their missing homework. This claim is true. Unfortunately, he also accuses some students who are telling the truth.
- What are the chances that a truthful student is accused?
- What are the chances that a student who is accused is actually telling the truth?
To let you explore this situation, we will provide the following data (Note, all of these figures are being provided as examples to allow you to explore the situation – we will use other assumptions in later steps.):
- Mr D receives excuses from 100 students
- 80% of these students are telling the truth
- Mr D correctly identifies and accuses 100% of lying students
We will also provide an answer to the first part of the question: the probability that a truthful student is accused is 0.2.
Questions like this can become quite complex. Use the comments to make sure that you have understood the scenario before moving on.