Compound events: find the number of outcomes

Learning Objectives Define compound events and identify their individual components. Systematically list all possible outcomes for a compound event using tables or lists. Construct and interpret tree diagrams to visualize and count outcomes for compound events. Apply the Fundamental Counting Principle to determine the total number of outcomes for compound events. Solve real-world problems involving finding the number of outcomes for compound events. Distinguish between individual event outcomes and compound event outcomes. Ever wonder how many different outfits you can make with just a few shirts and pants? 👕👖 Let's find out how to count all the possibilities when multiple choices are involved! In this lesson, you'll learn how to systematically count all the dif...

TermDefinitionExample EventA single action or happening with a measurable result. For example, flipping a coin is an event.Flipping a coin once; rolling a standard six-sided die. OutcomeA single possible result of an event. For example, 'heads' is an outcome when flipping a coin.Getting 'Heads' when flipping a coin; rolling a '3' on a die. Compound EventAn event that combines two or more simple events. The outcomes of a compound event are combinations of the outcomes of the individual events.Flipping a coin AND rolling a die; choosing a shirt AND a pair of pants. Sample SpaceThe set of all possible outcomes for an event or a compound event. It lists every single result that could happen.For flipping a coin and rolling a die, the sample space includes {H1, H2,...

Fundamental Counting Principle (for two events) If Event A has $n_A$ possible outcomes and Event B has $n_B$ possible outcomes, then the total number of outcomes for Event A followed by Event B is $N_{total} = n_A \times n_B$. Use this rule when you have two independent events and want to quickly find the total number of combined outcomes without listing them all. Simply multiply the number of outcomes for each individual event. Fundamental Counting Principle (for multiple events) If there are $k$ independent events, and the first event has $n_1$ outcomes, the second has $n_2$ outcomes, and so on, up to the $k$-th event having $n_k$ outcomes, then the total number of outcomes for the sequence of all $k$ events is $N_{total} = n_1 \times n_2 \times \dots \times n_k$. This is...