Compound events are events that consist of two or more simple events happening together. A tree diagram is a visual tool that helps you calculate the probabilities of these events. Each branch represents a possible outcome, and the probabilities are written along the branches. To find the probability of a sequence of events, you multiply the probabilities along the corresponding branches. Tree diagrams are especially useful when events are dependent (the outcome of one affects the outcome of the other) or independent (the outcome of one doesn't affect the other).
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Independent Events | A. A diagram used to represent the outcomes of a series of events. |
| 2. Dependent Events | B. The chance that an event will occur. |
| 3. Probability | C. Events where the outcome of one affects the outcome of the other. |
| 4. Tree Diagram | D. Events where the outcome of one does not affect the outcome of the other. |
| 5. Compound Event | E. An event that consists of two or more simple events. |
A ________ event consists of two or more simple events. A ________ is a visual tool used to determine the probabilities of outcomes. When events are ________, the outcome of one affects the outcome of the other. You ________ the probabilities along the branches to find the probability of a sequence of events. If the first event doesn't change the probability of the second, the events are considered ________.
Explain, in your own words, how a tree diagram can help you make better decisions when faced with multiple options and uncertain outcomes. Give a real-world example.
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