IGCSE Maths / Probability
The language of probability and the probability scale
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.
More lessons in Probability
- Listing outcomes systematically
- Theoretical probability and sample space
- Relative frequency and mutually exclusive events
- Expected frequency and relative frequency
- Multiplying independent probabilities
- At least one, and the complement
- Tree diagrams with replacement
- Tree diagrams without replacement
- Three stage tree diagrams
- Probability problem solving
- Conditional probability from a two way table
- Conditional probability from a Venn diagram
- Conditional probability without replacement
- Forming an equation from a probability