Sample Space
In probability theory, the sample space refers to the set of all possible outcomes of a random experiment
In probability theory, the sample space refers to the set of all possible outcomes of a random experiment. It is denoted as “S” and is a fundamental concept in understanding probability.
To better understand the concept of a sample space, let’s consider a simple example of rolling a fair six-sided die. The sample space for this experiment would be {1, 2, 3, 4, 5, 6}, as those are the possible outcomes of rolling the die.
In general, the sample space represents all possible outcomes, and it is important to define it accurately to properly analyze probabilities. Each outcome in the sample space is known as an “element” or a “sample point”. In the case of the die example, each number from 1 to 6 is a sample point.
It is worth mentioning that the sample space can consist of discrete or continuous elements depending on the nature of the experiment. For instance, in the case of flipping a fair coin, the sample space would be {Heads, Tails}, which represents two discrete outcomes.
The sample space forms the foundation for further calculations in probability theory, such as determining the probability of specific events or calculating the likelihood of certain outcomes. By studying and analyzing the sample space, we gain valuable insights into the probabilities associated with a particular experiment or situation.
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