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In probability theory, a sample space is the complete list of all possible outcomes of an experiment. Each outcome is called an elementary event. For instance, if you’re rolling a six-sided die, the sample space consists of the numbers {1, 2, 3, 4, 5, 6}. These are all the potential results of a single roll of the die.
Understanding the concept of a sample space is crucial because it forms the foundation for calculating probabilities. Whether you're dealing with rolling dice, flipping coins, or selecting cards from a deck, identifying the correct sample space ensures you're looking at all potential outcomes.

• A sample space can be finite or infinite.
• In finite sample spaces, the number of possible outcomes can be counted and is limited.
• In this exercise, the sample space consists of 275 equally likely events.

Finite probability refers to dealing with a sample space that is countable and limited, meaning there are a specific number of possible outcomes. When we talk about finite probability, the total probability of all outcomes will sum up to 1.
In our exercise example, the sample space has 275 outcomes, and this is considered finite because you can count the exact number of events.
To calculate the probability of an event happening in a finite sample space, we use the basic formula:\[P(E) = \frac{n(E)}{n(S)}\]where:

• \( P(E) \): Probability of event E
• \( n(E) \): Number of favorable outcomes for event E
• \( n(S) \): Total number of outcomes in the sample space

Since every elementary event in our problem is equally likely, we simplify this to \( P(E) = \frac{1}{n(S)} \). Thus, each elementary event in a sample space of 275 outcomes has a probability of \( \frac{1}{275} \).

An event is considered equally likely when each outcome in the sample space has an equal chance of occurring. This is a common assumption in many probability exercises because it simplifies calculations.
Consider flipping a fair coin. There are two possible equally likely outcomes: heads or tails. Each has a probability of \( \frac{1}{2} \).

In our exercise, the statement clearly indicates that all 275 events in the sample space are equally likely. This means:

• No outcome is favored over another.
• Each event will have the same probability, ensuring fairness and uniform distribution of chances.

By establishing that events are equally likely, you can proceed with straightforward probability calculations using the simple formula \( P(E) = \frac{1}{n} \), where \( n \) is the number of equally likely events, such as \( \frac{1}{275} \) in our exercise.