A sample space can be finite or infinite depending on the nature of the experiment.
In a simple coin toss, the sample space is {Heads, Tails}.
The notation for sample space is usually S or Ω.
Each outcome in a sample space is equally likely if the experiment is fair.
Sample spaces are foundational for defining events and calculating probabilities.
Review Questions
What is the sample space for rolling a six-sided die?
How do you denote the sample space in probability theory?
Explain why identifying the sample space is crucial in probability experiments.
Related terms
Event: A subset of a sample space; it consists of one or more outcomes.
Probability: A measure quantifying the likelihood that an event will occur, calculated as $P(E) = \frac{n(E)}{n(S)}$ where $n(E)$ is the number of favorable outcomes and $n(S)$ is the total number of possible outcomes.
Outcome: A single result from a probability experiment; each element within a sample space.