Maths - Perplexing probability

11th November 2011 at 00:00
It's a joy once you know how

On a cold and breezy Sunday afternoon, with a cup of tea in one hand and a red pen in the other, I found myself marking a stack of Year 7 assessment papers. The students had generally performed well. Then came Question 18. Paul has 15 T-shirts: 5 black, 3 white, 3 red, 2 dark blue, 1 light blue and 1 yellow.

Paul is going to take one of his T-shirts at random. What is the probability the T-shirt will: (a) be red; (b) not be black; (c) be light blue if Paul selects a blue T shirt?

Would anybody like to guess what the most common responses were from this bright bunch of Year 7s? "Not likely", "Quite likely", then "Sort of likely". I wanted to cry.

Probability is (probably) my favourite maths topic. I love the way that it is practical, useful, often surprising, and how it creeps into many parts of everyday life. However, I despair at how poorly it can be understood by even the brightest students. So I put my pen down, wiped away my tears and thought about how I would solve this problem if I was in charge of the World of Maths.

First, I would ban the use of "likely" and "unlikely" as a means of introducing students to probability. Who is to say what likely actually means? And once students are used to describing probabilities this way, it is incredibly difficult to wean them off it.

Second, I would ban the use of decimals and percentages to describe probabilities, and stick to fractions. In the question above, the reason that the answer to (a) is 315 is because three of the 15 T-shirts in Paul's colourful collection are red. Decimals and percentages make it harder for students to conceptualise. And if they struggle with place value or adding decimals, their journey to understanding probability is off track before it has even begun.

Finally, I would ban questions that do not make sense. "The probability Tony has chips for tea is 0.2." Good for Tony. But why is that the probability? The students may just be able to figure out that perhaps Tony has kept a record of his previous 10 teas and has had chips twice. Is this a good way of estimating probability? Before you know it, you are venturing into the areas of experimental probability, sampling, bias and independent events.

There are some amazing probability games, puzzles, lotteries and activities on TES Resources. They can help bring the subject to life, engaging students in a topic that they can relate to. Will all of this help students better understand probability and encourage them to enjoy the subject? I'd say it is quite likely.

Craig Barton is maths adviser to TES, a maths advanced skills teacher and creator of TES name: mrbartonmaths. Twitter: @mrbartonmaths


Craig recommends three resource collections to help with teaching probability:

- Topic Special - Probability

- Improving Learning in Mathematics: Mostly Statistics

- Mathematics Enhancement Program - GCSE

Find these collections and other resources at


In the forums

Teachers discuss the whys and wherefores of teaching probability - what's your stance?

And in another thread a teacher asks about using probability to determine the sex of a baby

All resources and links at


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