Probability questions are a favourite in the non-calculator papers, particularly towards the end of the paper. They usually involve two random events and the question asks you to work out the probability of a certain outcome. And, of course, you must pay particular attention to the language in the question as to what this ‘certain outcome’ is. Such questions are often best done using a probability tree diagram.

What I’ve given below is a list of things to watch out for when drawing and using probability tree diagrams. So, right at the start, I’m assuming you already have some knowledge of these tree diagrams. At the end I have given one example.

1. You need to decide from the question whether the probability they want you to find is a ‘with replacement’ or a ‘without replacement’ situation.

- if ‘with replacement’, then the values of the probabilities will NOT change along the branches from one event to the next.
- if ‘without replacement’, then the values of the probabilities WILL change along the branches from one event to the next.

2. Usually the number of branches for the number of possible outcomes is 2, sometimes 3, but however many there are you must make sure that the probabilities you write down on each branch ALL ADD UP TO ONE WHOLE.

3. To find the probability of one outcome followed by another outcome, we must multiply the probabilities ALONG THE BRANCHES.

4. If the question asks you to find the probability that the final outcome of some event is the same colour (for example), then you must look for ALL the outcomes that have the same colour, find the probability of each one, and then ADD these probabilities together.

5. Don’t forget ‘ (Not P) = P – 1’

Suppose in a game there was only 1 way to Win but 3 ways to Lose, and the question asked you to work out the chance of losing (‘Not’ Winning). Well, you could do this the hard way and work out the probability of each ‘Lose’ outcome and then ADD them up. But a quicker way is to work out the chance of Winning (which is just 1 calculation, not 3 separate calculations) and then subtract 1 from the answer, because….

Probability of NOT Winning = Probability of Winning – 1