Probability

Basics of Probability

• Probability refers to the measure of likelihood that an event will occur.
• It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.
• Probability values range from 0 to 1. A probability of 0 means an event is impossible and a probability of 1 means an event is certain.

Key Terminology

• An event is any collection of outcomes of an experiment.
• A simple event is an event that can’t be broken down further.
• A compound event is an event that includes more than one simple event.
• Independent events are those whose outcomes don’t influence each other.
• Dependent events are those whose outcomes do affect each other.

Rules of Probability

• The Multiplication rule states that the probability of two independent events occurring is the product of their individual probabilities.
• The Addition rule states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities.
• Conditional probability is the probability of an event given that another event has occurred.

Probability Distributions

• A probability distribution is a table or graph that assigns probabilities to each possible outcome of a random experiment.
• Binomial distribution and normal distribution are two commonly used probability distributions in statistics.

Importance & Relevance

• Knowing how to calculate probabilities can help make informed decisions based on data.
• Understanding probability distributions can aid in the prediction of future events.
• Concepts of probability underpin many fields of study, including economics, finance, insurance, psychology, and meteorology.

Tips

• In questions involving “and”, consider whether the events are independent. If so, multiply the probabilities; if not, use conditional probability.
• In questions involving “or”, use the addition rule, but remember to subtract the probability of both events occurring if they are not mutually exclusive.