In probability, two events are considered independent if the outcome of one does not affect the outcome of the other. When calculating the probability of two independent events both occurring, you multiply their individual probabilities. For example, if the probability of event A is $\frac{1}{2}$ and the probability of event B is $\frac{1}{3}$, then the probability of both A and B occurring is $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$. Understanding independent events is crucial for solving many probability problems.
This worksheet will test your understanding of calculating the probability of independent events. Get ready to apply what you've learned!
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Independent Events | a. A result of a probability experiment |
| 2. Probability | b. Events where the outcome of one does not influence the outcome of the other |
| 3. Outcome | c. The set of all possible outcomes |
| 4. Sample Space | d. A measure of the likelihood that an event will occur |
| 5. Event | e. A set of outcomes to which a probability is assigned |
Complete the following paragraph using the words: independent, multiply, probability, outcome, events.
When calculating the ________ of two ________ ________, you ________ their individual probabilities. This is because the ________ of one event does not affect the ________ of the other.
Give an example of two real-world independent events and explain why they are independent.
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