Question of the Week 1: Probability Tree Diagrams

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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.

Answer d)
is the correct answer

In the 5 minutes it took me to ask my Year 11s this question, them to vote with their fingers for their choice of answer, and then listen to them make the cases for each of their answers, I learnt so much about the areas I needed to focus on during that lesson - multiplying decimals, as it turned out! The students also learnt loads from listening to each other's explanations and justifications. Furthermore, even though no-one selected Answer d), it led to a really interesting discussion about why it was one of the options.

A really lovely question, and thanks so much to JCMurphy for uploading it

To access the question to see statistics for each answer, to include it in a quiz, download it for offline use, embed it in a blog, or loads more, just click here.And if you have used the question, or have any thoughts or comments about it - perhaps you would include a different incorrect answer - then please share your comments below. And please consider creating a question yourself on the website!