Understanding probability

Learning Objectives Define key probability terms: outcome, event, sample space, and favorable outcome. Identify all possible outcomes and favorable outcomes for a given simple event. Calculate the theoretical probability of a simple event as a fraction, decimal, or percentage. Describe the likelihood of an event using terms like impossible, unlikely, equally likely, likely, and certain. Compare the probabilities of different events to determine which is more or less likely. Apply probability concepts to simple real-world scenarios. Have you ever wondered what your chances are of winning a game or if it will rain tomorrow? 🎲 In this lesson, you'll discover how to measure the likelihood of events happening. Understanding probability helps us make predictions, analyze da...

TermDefinitionExample ProbabilityThe measure of how likely an event is to occur. It's a number between 0 and 1, inclusive.The probability of flipping a coin and getting heads is 1/2. OutcomeA single possible result of an experiment or situation.When rolling a standard die, 'rolling a 3' is an outcome. EventA specific outcome or a set of outcomes that you are interested in.When rolling a standard die, 'rolling an even number' is an event (outcomes: 2, 4, 6). Sample SpaceThe set of all possible outcomes of an experiment.For rolling a standard die, the sample space is {1, 2, 3, 4, 5, 6}. Favorable OutcomeAn outcome that meets a specific condition for an event.If the event is 'rolling an even number', the favorable outcomes are {2, 4, 6}. Impossible EventAn...

Probability Formula for Simple Events $P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ This formula is used to calculate the theoretical probability of a simple event. 'P(event)' stands for 'the probability of the event'. Probability Range $0 \le P(\text{event}) \le 1$ The probability of any event must be a number between 0 and 1, inclusive. A probability of 0 means the event is impossible, and a probability of 1 means the event is certain. Complementary Events $P(\text{event}) + P(\text{not event}) = 1$ The probability of an event happening plus the probability of the event not happening always equals 1. This can be useful for finding the probability of an event not occurring.