Sample Space
In probability theory, a sample space refers to the set of all possible outcomes of an random experiment or event
In probability theory, a sample space refers to the set of all possible outcomes of an random experiment or event. It is denoted by the symbol S.
To understand the concept of a sample space, let’s consider an example. Suppose you are rolling a fair six-sided die. The sample space for this experiment would consist of all possible outcomes when the die is rolled. In this case, the sample space would be {1, 2, 3, 4, 5, 6}, since these are the possible values that can appear on the face of the die.
Another example could be flipping a coin. The sample space for this experiment would consist of two possible outcomes: {Heads, Tails}.
The concept of a sample space is important in probability theory because it allows us to define events and calculate probabilities. An event is a subset of the sample space, meaning it consists of one or more outcomes. For example, in the die rolling experiment, an event could be rolling an even number, which corresponds to the subset {2, 4, 6}.
The concept of a sample space helps us analyze and understand the probabilities associated with different outcomes. It is a fundamental concept in probability theory and provides a framework for conducting probability calculations.
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