Probability definition
Probability is a measure of how likely something is to happen. It can be written as a fraction, decimal or percentage. A probability of 0 means an event is impossible, and a probability of 1 means an event is certain. Values between 0 and 1 show different levels of likelihood. For example, a probability of 1 over 2 means an event has an even chance of happening.
A simple example is tossing a fair coin. There are two possible outcomes: heads and tails. The probability of getting heads is 1 out of 2, or 1 over 2, because one of the two equally likely outcomes is heads. This can also be written as 0.5 or 50%. These three forms represent the same probability.
Probability is used in statistics, data handling, games, science, weather forecasts, insurance, finance, medicine, surveys and real-life decision making. At GCSE level, students calculate probabilities from equally likely outcomes, tables, frequency data, Venn diagrams and tree diagrams. They also compare experimental probability with theoretical probability and use probability to describe uncertainty.
The basic formula is probability equals number of favourable outcomes divided by total number of possible outcomes. For example, if a bag contains 3 red counters and 7 blue counters, there are 10 counters in total. The probability of choosing a red counter is 3 over 10. The probability of choosing a blue counter is 7 over 10. The probabilities add to 1 because one of the colours must be chosen.
A sample space is a list of all possible outcomes. For a normal six-sided die, the sample space is 1, 2, 3, 4, 5 and 6. The probability of rolling an even number is 3 over 6 because the even outcomes are 2, 4 and 6. This simplifies to 1 over 2. Listing the sample space helps students make sure no outcomes are missed or counted twice.
Experimental probability is based on results from an experiment or trial. For example, if a spinner lands on green 18 times out of 60 spins, the experimental probability of green is 18 over 60, which simplifies to 3 over 10. Theoretical probability is based on the expected chance from the structure of the situation, such as a fair spinner with equal sections. Experimental results can vary, especially when the number of trials is small.
Probability can also describe combined events. Tree diagrams help show possible outcomes when more than one event happens, such as choosing a counter and then choosing another counter. Venn diagrams help organise probabilities involving groups and overlaps. These methods become useful when simple counting is not enough and the structure of the problem needs to be shown clearly.
Related ideas include likelihood, outcomes, sample space, fractions, decimals, percentages, relative frequency, experimental probability, theoretical probability, tree diagrams and Venn diagrams. A clear definition of probability helps students understand that probability is not a guess. It is a mathematical way of measuring uncertainty and making predictions from information.