Compound Event — Definition, Formula & Examples
A compound event is an event that consists of two or more simple events happening together or in sequence. For example, rolling a die and flipping a coin at the same time is a compound event.
A compound event is a subset of a sample space that can be decomposed into the union, intersection, or sequential combination of two or more simple (single-outcome) events. Its probability is determined by applying the addition rule, multiplication rule, or a combination of both, depending on the relationship between the component events.
How It Works
To find the probability of a compound event, first identify the simple events involved. Then determine whether the events are independent (one does not affect the other) or dependent. For independent events, multiply the individual probabilities. If the compound event uses "or," apply the addition rule instead: add the individual probabilities and subtract the overlap. Listing outcomes in a table, tree diagram, or organized list helps you count the favorable outcomes in the sample space.
Worked Example
Problem: You roll a standard six-sided die and flip a fair coin. What is the probability of rolling a number greater than 4 AND getting heads?
Identify the simple events: Simple event A: rolling greater than 4 (outcomes 5 or 6). Simple event B: getting heads.
Check independence and multiply: The die roll does not affect the coin flip, so the events are independent. Multiply their probabilities.
Answer: The probability of rolling greater than 4 and getting heads is , or about 16.7%.
Why It Matters
CCSS 7.SP.8 asks you to find probabilities of compound events using lists, tables, and tree diagrams. Understanding compound events is also essential in real contexts like predicting weather patterns (rain AND wind) or calculating odds in games that involve multiple actions.
Common Mistakes
Mistake: Adding probabilities when you should multiply them.
Correction: Use multiplication when both events must occur ("and"). Use addition when at least one event must occur ("or"). The connecting word tells you which operation to apply.