Understanding Probability Theory: Exploring Sample Spaces and Their Significance in Calculating Event Probability

Sample Space

In probability theory, the sample space refers to the set of all possible outcomes of an experiment or random event

In probability theory, the sample space refers to the set of all possible outcomes of an experiment or random event. It is denoted by the symbol “S”.

To understand the concept of a sample space, let’s consider an example. Suppose you want to toss a fair coin. The possible outcomes of this experiment are getting a “Heads” or getting a “Tails”. Therefore, the sample space for this experiment would be {H, T}.

Similarly, let’s consider rolling a fair six-sided die. The possible outcomes in this case are getting any of the six numbers from 1 to 6. Therefore, the sample space for this experiment would be {1, 2, 3, 4, 5, 6}.

In some cases, the sample space can be finite, such as the examples above. However, it can also be infinite. For example, if you consider flipping a fair coin until you get a “Heads”, the sample space would be {H, TH, TTH, TTTH, …}, which represents an infinite set of possible outcomes.

It is important to note that the sample space includes all possible outcomes, even those that are unlikely or impossible. Each outcome in the sample space should be unique and mutually exclusive, meaning that only one outcome can occur at a time.

The concept of a sample space is fundamental in probability theory as it allows us to calculate the probability of different events occurring by comparing the number of favorable outcomes to the total number of possible outcomes in the sample space.

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