Probability

Basics of Probability

• Probability refers to the likelihood of an event occurring.
• Probabilities are usually expressed as fractions, decimals, or percentages.
• Probability is always between 0 and 1, inclusive. A probability of 0 means the event cannot happen, and a probability of 1 means that the event is certain to happen.

Simple Events

• A simple event is an outcome or an event that cannot be further broken down into simpler components.
• The sum of the probabilities of all possible outcomes (simple events) is equal to 1.

Compound Events

• Compound events involve the probability of two or more events happening together.
• If two events, A and B, are independent, the probability of both events occurring is the product of the probabilities of each event. This is known as the Multiplication Rule for independent events: P(A and B) = P(A) x P(B).
• If the events are dependent, you have to adjust for the fact that the first event changes the probability of the second event.

The Addition Rule

• The Addition Rule is used when you’re looking for the probability that any one of multiple events will happen.
• For mutually exclusive events (events that cannot occur at the same time), the Addition Rule states that P(A or B) = P(A) + P(B).
• For events that are not mutually exclusive, you must correct for the overlap: P(A or B) = P(A) + P(B) - P(A and B).

Conditional Probability

• Conditional probability is the likelihood of an event given that another event has already occurred. It’s represented as **P(A

  B)**, which is read as “the probability of A given B.”

• P(A	B) is calculated as P(A and B) / P(B).

Complementary Events

• The complement of an event A (noted as A’) is the event not occurring.
• The sum of the probabilities of an event and its complement is equal to 1: P(A) + P(A’) = 1.

Remember to use diagrams like two-way tables and tree diagrams to help visualise and solve probability problems.