IGCSE Maths / Probability

The language of probability and the probability scale revision notes

Edexcel International GCSE Maths (4MA1), chapter 20: Probability, specification point 6.3a-f. Free lesson.

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Probability measures how likely an event is, using a number from 0 to 1. You can calculate it by comparing the outcomes you want with all the equally likely outcomes, and use the scale to describe how likely the event is.

What a probability means

A probability is the number of outcomes you want divided by the total number of equally likely outcomes. It is a part of a whole, so it cannot be less than 0 or greater than 1. You can write it as a fraction, decimal or percentage. A probability of 0 means the event is impossible. A probability of 1 means the event is certain. Odds wording such as “3 to 7” is not an accepted way to write a probability.

Where probability words sit on the scale

The scale runs from 0 to 1. The words describe where an event sits on that scale, with 0.5 marking an even chance. Impossible: probability 0. It cannot happen. Unlikely: probability between 0 and 0.5. It probably will not happen. Even chance: probability 0.5. It is as likely to happen as not. Likely: probability between 0.5 and 1. It probably will happen. Certain: probability 1. It must happen.

How to calculate a probability

Put the number of outcomes you want on top and the total number of outcomes underneath. Count the whole group first, because the denominator must include every possible outcome.

How to find the probability of something not happening

If an event either happens or does not happen, those two possibilities cover everything. Their probabilities add to 1, so you can find the probability of the event not happening by subtracting its probability from 1. P(not happening) = 1 − P(happening). For example, if P(rain) = 0.3, then P(no rain) = 1 − 0.3 = 0.7.

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