Simple Event — Definition, Formula & Examples
A simple event is an outcome of a probability experiment that cannot be broken down any further. For example, rolling a 4 on a standard die is a simple event because it is a single, specific result.
A simple event is an event consisting of exactly one outcome in the sample space of a probability experiment. It is a singleton subset of the sample space.
Key Formula
Where:
- = Probability of the simple event E
- = Total number of equally likely outcomes in the sample space
How It Works
When you perform a probability experiment, the sample space lists every possible outcome. Each individual outcome on its own is a simple event. To find the probability of a simple event, you divide 1 by the total number of equally likely outcomes. If outcomes are not equally likely, each simple event has its own assigned probability, and the probabilities of all simple events in the sample space must add up to 1.
Worked Example
Problem: A standard die is rolled once. What is the probability of the simple event "rolling a 3"?
Identify the sample space: A standard die has 6 faces, so the sample space is {1, 2, 3, 4, 5, 6}.
Apply the formula: Rolling a 3 is one specific outcome out of 6 equally likely outcomes.
Answer: The probability of rolling a 3 is .
Why It Matters
Simple events are the building blocks of all probability calculations. When you study compound events — like rolling an even number — you are really combining simple events. Understanding them first makes more advanced topics like conditional probability much easier to grasp.
Common Mistakes
Mistake: Confusing a simple event with a compound event. For example, calling "rolling an even number" a simple event.
Correction: "Rolling an even number" includes three outcomes (2, 4, 6), so it is a compound event. A simple event has exactly one outcome, such as "rolling a 4."