Compound events: find the number of outcomes

Learning Objectives Define and identify compound, independent, and dependent events. Construct tree diagrams and organized lists to represent the sample space of a compound event. Apply the Fundamental Counting Principle to calculate the total number of outcomes. Differentiate between problems with replacement and without replacement. Calculate the total number of outcomes for multi-stage experiments. Solve real-world problems involving the number of outcomes for compound events. Ever wonder how many different outfit combinations you could make from your closet, or how many different pizza topping combinations are possible? 👕🍕 Let's find out! This tutorial will teach you how to systematically count the total number of possible results, or 'outcomes,' for si...

TermDefinitionExample OutcomeA single possible result of a probability experiment.When rolling a standard six-sided die, one possible outcome is rolling a 4. Sample SpaceThe set of all possible outcomes of an experiment.The sample space for flipping a coin is {Heads, Tails}. Simple EventAn event consisting of only one outcome.Drawing the ace of spades from a standard deck of 52 cards. Compound EventAn event that consists of two or more simple events.Flipping a coin AND rolling a die. The outcome (Heads, 6) is one result of this compound event. Independent EventsTwo events where the outcome of the first event does NOT affect the outcome of the second event.Flipping a coin and then rolling a die. The coin's result doesn't change the die's possible outcomes. Dependent EventsTw...

The Fundamental Counting Principle (Multiplication Rule) If event A has $m$ possible outcomes and event B has $n$ possible outcomes, then there are $m \times n$ total possible outcomes for event A followed by event B. This is the primary method for finding the total number of outcomes without listing them all. Use it when an experiment consists of multiple stages or parts. Simply multiply the number of outcomes for each stage. Tree Diagrams A visual method to list all possible outcomes of a compound event. Each 'branch' represents a possible outcome for a simple event. Use this method when you need to see and list every single possible outcome, not just the total number. It is most effective for experiments with a small number of stages and outcomes.