Combined Probability

Key Facts and Exam Tips

The probability of something happening is expressed as a number (fraction or decimal) between 0 and 1.

If something is impossible then its probability is 0.

If something is bound to happen then its probability is 1.

(probability of a favourable outcome) = (number of favourable outcomes) ÷ (total number of possible outcomes)

The probability of an event not happening is one minus the probability that it will happen.

Two outcomes are ‘mutually exclusive’ if one outcome prevents the other from happening.

The sum of the probabilities of all possible (mutually exclusive) outcomes of an event is one. You can use this fact to check that you have covered all possibilities and that you have calculated the probabilities correctly.

To find the combined probability of either one or another event, if the events are mutually exclusive, you add the probabilities.

Two events are independent if knowing the outcome of one does not affect the probability of the other.

To find the combined probability of both one and another event, if the events are independent, you multiply the probabilities.

Make sure you know how to add and how to multiply fractions.

If a question states probabilities as fractions, you should use fractions in your answer.

Tree diagrams help to show all possible events or combinations of events. You can write both the events and their probabilities on the diagram.

Make sure you allow plenty of space for your diagram, particularly if you are going to show more than one event.

Learn how to read along the branches to identify combinations of events. The combined probabilities are calculated by multiplying the individual probabilities along the branches.

When combining two or more events on a tree diagram, it is usually helpful to record all the possible outcomes, with their combined probabilities, and then select the ones relevant to the question.