Probability Basics

Understanding Probability Basics

• Probability is a measure of the likelihood of an event happening. It is presented as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.
• An event refers to the outcome or outcomes of interest in a probability situation.
• The sample space of an experiment or random trial is the set of all possible outcomes.
• A trial is an instance of a random experiment or process. The result is called an outcome.

Probability Notations and Definitions

• The probability of an event is denoted as P(A) where ‘A’ is the event of interest.
• Complementary events are events that complete the sample space when paired together. If ‘A’ is an event, ‘not A’ is its complement. Therefore, P(A) and P(not A) always add up to 1.
• Independent events are those whose outcome doesn’t affect the probability of the other. If ‘A’ and ‘B’ are independent events, then the probability of both events happening, P(A ∩ B), is the product of their individual probabilities, i.e., P(A)⋅P(B).

• Dependent events are events where the outcome of the first event affects the probability of the second event. If ‘A’ and ‘B’ are dependent events, then P(A ∩ B) = P(A)⋅P(B

  A), where P(B

  A) is the probability of event ‘B’ happening given that ‘A’ has occurred.

Calculating Probability

• Experimental probability is based on the results of an actual experiment. It is calculated as the number of times event ‘A’ occurred divided by the number of trials.
• Theoretical probability is derived from mathematical models. It is calculated as the number of favourable outcomes divided by the total number of outcomes in the sample space.

Understanding Probability in Context

• Probability has applications in a range of fields including science, business, politics and even sports.
• Misinterpretation or misuse of probability can lead to incorrect conclusions or predictions.
• Always question the source and calculations of probabilities in real-life situations.