Question of the Week 1: Probability Tree Diagram

The following question is taken from my website Diagnostic Questions. Here you will find 1000s of high quality maths questions, ideal for assessment for learning, which have been created and shared by maths teachers all over the world.

I love this question. Tree Diagrams are a very popular question on GCSE exams, they carry a significant number of marks, most students find them pretty straight forward, and yet there are countless opportunities to make some very costly mistakes that result from misconceptions students might have.

This question helps me as a teacher identify those misconceptions my students may have very quickly. Therefore, it helps me decide if I need to spend more time going over Tree Diagrams -and exactly which aspects I need to focus on – without having to spend 15 minutes waiting for students to draw one from scratch.

Having asked the question, let’s see what we might learn from our students’ responses:

Answer a) might suggest they have attempted to multiply the two probabilities together, but have a misconception when it comes to multiplying two decimals together.

Answer b) is a classic. This is where students have decided to add the two probabilities instead of multiplying them

Answer c) is an interesting one. Students selecting this answer may believe that as there are 4 possible outcomes, each one is equally likely, and hence the probability of each is 0.25