Introduction to Probability Probability is a fundamental concept in statistics that measures the likelihood of an event occurring. In GCSE Mathematics, students...
Probability is a fundamental concept in statistics that measures the likelihood of an event occurring. In GCSE Mathematics, students learn to work with theoretical and experimental probabilities, as well as various techniques for representing and analyzing probability problems.
Probabilities are expressed on a scale from 0 to 1, where:
Theoretical probability is calculated based on the total number of possible outcomes and the number of favorable outcomes:
Probability of an event = Number of favorable outcomes / Total number of possible outcomes
Problem: If a fair die is rolled, what is the probability of rolling a 5?
Solution:
Experimental probability is calculated by performing an experiment and recording the outcomes. As the number of trials increases, the experimental probability should approach the theoretical probability.
Various diagrams and tables are used to represent probability problems, including:
Independent events are events where the outcome of one event does not affect the probability of the other event occurring. Dependent events are events where the outcome of one event affects the probability of the other event occurring.
Conditional probability is the probability of an event occurring given that another event has already occurred. Tree diagrams are used to represent and calculate probabilities of combined independent events.
For more detailed information and practice questions, refer to the AQA GCSE Mathematics specification and resources from trusted educational websites like BBC Bitesize.