Question

What is the definition of a compound event in probability?

Ask by Weber Pritchard. in the United States
Jan 20,2025

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Answer

A compound event in probability is an event made up of two or more simple events combined using "and" or "or." For example, rolling an even number on a die or drawing a heart or a face card from a deck.

Solution

A compound event in probability is an event that consists of two or more simple events. Simple events are the most basic outcomes that cannot be broken down further. A compound event can be formed by combining simple events using logical operations such as "and" (intersection) or "or" (union). For example: - If you roll a die, the simple events could be rolling a 1, 2, 3, 4, 5, or 6. A compound event could be rolling an even number (which includes the simple events of rolling a 2, 4, or 6). - Another example could be drawing a card from a deck. The simple events are drawing each individual card, while a compound event could be drawing a heart or a face card. In summary, a compound event encompasses multiple outcomes and can be analyzed using the principles of probability to determine the likelihood of its occurrence.

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The Deep Dive

A compound event in probability is when you combine two or more simple events. Think of it like a tasty smoothie: you take different fruits (events) and blend them together to create something new with its own flavor (probability). For instance, if you roll a die and flip a coin, you're looking at a compound event that involves the outcomes of both the die roll and the coin flip! To make the concept even juicier, consider how compound events can be independent or dependent. Independent events don't affect each other—like flipping a coin and rolling a die. In contrast, dependent events are linked; for example, drawing cards from a deck without replacement impacts the remaining cards. Understanding this difference can make calculating probabilities a lot smoother!

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