Lesson 4: Compound Events: Tree Diagrams

Property

A tree diagram systematically displays all possible outcomes of compound events by creating branches for each outcome of the first event, then extending branches for each outcome of subsequent events from every existing branch.

Examples

Property

The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes. A tree diagram helps visualize all possible outcomes of a compound event.

Examples

• A coin is tossed twice. The tree diagram shows 4 possible outcomes: HH, HT, TH, TT. The probability of getting exactly one tail is $\frac{2}{4}$ or $\frac{1}{2}$, as there are two favorable outcomes (HT, TH).
• A number cube is rolled and a coin is tossed. The tree diagram shows 12 possible outcomes. The probability of rolling a number less than 3 and tossing heads is $\frac{2}{12}$ or $\frac{1}{6}$, as there are two favorable outcomes (1H, 2H).

Explanation

A tree diagram is a tool used to map out the sample space of a compound event. Each unique path from the start to an endpoint of the diagram represents one possible outcome. To find the probability of a specific event, count the number of paths that meet the event''s criteria (favorable outcomes) and divide by the total number of paths (total outcomes).