sample point — Definition, Formula & Examples
A sample point is one individual outcome in a probability experiment. For example, when you roll a die, each face (1, 2, 3, 4, 5, 6) is a separate sample point.
A sample point (or elementary outcome) is an element of the sample space of a random experiment. Every event is a subset of sample points, and the sample points are mutually exclusive and collectively exhaustive — exactly one occurs on each trial.
Worked Example
Problem: Two coins are flipped. List all the sample points and find the probability of the event "at least one head."
List the sample points: Each sample point is one possible outcome of flipping two coins.
Identify the event: "At least one head" includes every sample point that contains an H.
Compute the probability: With equally likely sample points, divide the number of favorable points by the total.
Answer: There are 4 sample points. The probability of at least one head is .
Why It Matters
Listing sample points is the first step when you build a sample space, which is the foundation for calculating any probability. In courses like AP Statistics, clearly identifying sample points prevents counting errors in problems involving combinations of events.
Common Mistakes
Mistake: Confusing a sample point with an event.
Correction: A sample point is a single outcome; an event is a set of one or more sample points. For instance, rolling a 3 is a sample point, while rolling an odd number is an event containing the sample points {1, 3, 5}.