Compound events - find the number of outcomes by counting

Learning Objectives Define a compound event and distinguish it from a simple event. Construct organized lists to represent the sample space of a compound event. Create tree diagrams to visualize and count the total number of outcomes for a compound event. State and apply the Fundamental Counting Principle to efficiently calculate the number of outcomes. Solve multi-step real-world problems by breaking them down into a sequence of simple events. Interpret the sample space of a compound event to answer specific questions about outcomes. How many different pizza combinations can you create with 3 crusts, 2 sauces, and 5 toppings? 🍕 Let's find out without listing them all! This tutorial will introduce you to compound events, which are made up of two or more simple events....

TermDefinitionExample OutcomeA single possible result of an experiment or action.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.Choosing the color blue from a set of colored pencils. Compound EventAn event that consists of two or more simple events happening in sequence or together.Flipping a coin AND rolling a die. The outcome (Heads, 4) is one result of this compound event. Organized ListA systematic method of listing all possible outcomes of a compound event.For flipping a coin twice, the organized list is: HH, HT, TH, TT. Tree DiagramA diagram that uses branches to show all possible outcom...

The Fundamental Counting Principle (Two Events) Total Outcomes = m × n If a first event can occur in 'm' ways and a second event can occur in 'n' ways, you can find the total number of outcomes for the compound event by multiplying m and n. This is the most efficient way to count outcomes. The Generalized Fundamental Counting Principle Total Outcomes = n_1 × n_2 × n_3 × ... × n_k If a compound event consists of a sequence of 'k' events, and the first event has n_1 outcomes, the second has n_2 outcomes, and so on, the total number of outcomes is the product of the number of outcomes of each individual event.