Theoretical probability

Learning Objectives Define experiment, outcome, sample space, and event. Determine the sample space for a simple or compound experiment. Calculate the theoretical probability of a single event and express it as a fraction, decimal, and percent. Explain that the probability of an event is a number between 0 and 1, inclusive. Apply the complement rule to find the probability that an event will not occur. Calculate the theoretical probability of simple compound events, such as flipping two coins or rolling two dice. If you roll a standard six-sided die, are you more likely to roll a 6 or a number less than 3? 🎲 Let's figure out what *should* happen! This tutorial introduces theoretical probability, which is a way to predict the likelihood of an event based on reasoning a...

TermDefinitionExample ExperimentAn action or process with an uncertain result that can be repeated.Flipping a coin, rolling a die, or drawing a card from a deck. OutcomeA single possible result of an experiment.When rolling a die, one possible outcome is rolling a 4. Sample Space (S)The set of all possible outcomes of an experiment. It is often written using set notation { }.The sample space for rolling a standard six-sided die is S = {1, 2, 3, 4, 5, 6}. Event (E)A specific outcome or a collection of outcomes from an experiment that you are interested in.When rolling a die, the event of 'rolling an odd number' corresponds to the outcomes {1, 3, 5}. Favorable OutcomeAn outcome that satisfies the conditions of the event.For the event 'rolling an odd number' on a die, the...

Theoretical Probability Formula P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} Use this formula to calculate the probability of an event E when all outcomes in the sample space are equally likely. The Range of Probability 0 \le P(E) \le 1 The probability of any event E is always 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. The Complement Rule P(E') = 1 - P(E) The probability that an event will not occur is 1 minus the probability that it will occur. This is often easier than counting all the outcomes for 'not E'.