In the die-rolling experiment, if S={1,2,3,4,5,6}, A={ even number }, B={ number ≥2}, C={ number

step 1 Okay, so for this problem, we're rolling a dye. And so we want to first state what our sample si

In the die-rolling experiment, if S={1,2,3,4,5,6}, A={ even...

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Key Concepts

Event and Union of Events

An event is a specific set of outcomes from the sample space, and the union of events represents all outcomes that belong to at least one of the events. Understanding how multiple events can combine through unions is fundamental to calculating probabilities in overlapping cases.

Sample Space

The sample space of an experiment is the complete set of all possible outcomes. In probability theory, defining the sample space is essential because every event is a subset of this space, and the probabilities of events are determined relative to it.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a combinatorial method used to calculate the probability of the union of several events. It corrects for overcounting by subtracting the probabilities of intersections of events and, when necessary, adding back in the probabilities of intersections of three or more events. This principle ensures that all overlapping cases are appropriately accounted for in the final probability calculation.

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