Pregunta

What is the definition of a compound event in probability?

Ask by Colon Reeves. in South Africa
Jan 23,2025

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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 queen from a deck.

Solución

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 are the outcomes {1, 2, 3, 4, 5, 6}. A compound event could be rolling an even number, which includes the simple events {2, 4, 6}. - Another example of a compound event could be drawing a card from a deck and getting either a heart or a queen. This event combines the simple events of drawing any heart (13 outcomes) and drawing any queen (4 outcomes, but one of them is a heart, so it counts only once). In summary, a compound event is a combination of two or more simple events, and it can be analyzed using the rules of probability to determine its likelihood.

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The Deep Dive

A compound event in probability refers to an event that combines two or more simple events, which are the outcomes of individual experiments. For example, rolling a die and flipping a coin at the same time creates a compound event, where you need to consider the outcomes of both the die and the coin together—such as getting a 3 on the die and heads on the coin. In real-world scenarios, compound events are everywhere! Think about weather forecasts: predicting rain and high temperatures creates a compound event. Simultaneously knowing these outcomes helps people plan their activities, like whether to take an umbrella or wear shorts. This interplay of events illustrates the practical importance of understanding and calculating compound events in daily life.

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