Outcome

Outcome

A single, specific possible result of an experiment.

Experiment	Outcomes
Tossing a coin	heads, tails
Rolling a six-sided die	1, 2, 3, 4, 5, 6
Tossing a coin AND rolling a six-sided die	(heads, 1), (heads, 2), (heads, 3), (heads, 4), (heads, 5), (heads, 6), (tails, 1), (tails, 2), (tails, 3), (tails, 4), (tails, 5), (tails, 6)

See also

Sample space, event, probability

Key Formula

P(\text{outcome}) = \frac{1}{n}

Where:

$P(\text{outcome})$ = Probability of any single outcome when all outcomes are equally likely
$n$ = Total number of possible outcomes in the sample space

Worked Example

Problem: A standard six-sided die is rolled once. List all outcomes, then find the probability of a single outcome (rolling a 4).

Step 1: Identify the experiment: rolling one six-sided die.

Step 2: List every outcome. Each face of the die is one outcome.

\{1,\, 2,\, 3,\, 4,\, 5,\, 6\}

Step 3: Count the total number of outcomes.

n = 6

Step 4: Because the die is fair, every outcome is equally likely. Apply the formula to find the probability of rolling a 4.

P(4) = \frac{1}{6}

Answer: There are 6 outcomes. The probability of the single outcome "rolling a 4" is

\frac{1}{6} \approx 0.167

Another Example

This example shows a compound experiment with two actions performed together, where each outcome is an ordered pair rather than a single value. It demonstrates how the counting principle determines the total number of outcomes.

Problem: A coin is tossed and a six-sided die is rolled at the same time. How many outcomes are there in total, and what is the probability of the outcome (heads, 3)?

Step 1: Identify the two parts of the experiment: one coin toss (2 outcomes) and one die roll (6 outcomes).

Step 2: Use the counting principle to find the total number of outcomes. Multiply the outcomes of each part.

n = 2 \times 6 = 12

Step 3: List the outcomes as ordered pairs. Each pair combines one coin result with one die result.

\{(H,1),\,(H,2),\,(H,3),\,(H,4),\,(H,5),\,(H,6),\,(T,1),\,(T,2),\,(T,3),\,(T,4),\,(T,5),\,(T,6)\}

Step 4: Since both the coin and die are fair, all 12 outcomes are equally likely. Find the probability of (heads, 3).

P(H,3) = \frac{1}{12}

Answer: There are 12 outcomes. The probability of the single outcome (heads, 3) is

\frac{1}{12} \approx 0.083

Frequently Asked Questions

What is the difference between an outcome and an event in probability?

An outcome is one single, indivisible result of an experiment — like rolling a 5 on a die. An event is a set of one or more outcomes grouped together by some condition, such as "rolling an odd number" (the set {1, 3, 5}). Every outcome is technically an event by itself, but not every event is a single outcome.

What is the difference between an outcome and a sample space?

An outcome is one specific result, while the sample space is the complete set of all possible outcomes for an experiment. For example, when you flip a coin, "heads" is an outcome, and {heads, tails} is the sample space. Think of an outcome as one element and the sample space as the entire collection.

Can outcomes be equally likely or not equally likely?

Outcomes can be either. A fair coin gives two equally likely outcomes (each with probability

\frac{1}{2}

). A weighted coin, however, might land on heads 70% of the time, making the outcomes unequally likely. The formula

P = \frac{1}{n}

only applies when all outcomes are equally likely.

Outcome vs. Event

	Outcome	Event
Definition	A single, specific result of an experiment	A set of one or more outcomes
Example (rolling a die)	Rolling a 3	Rolling an even number: {2, 4, 6}
Size	Always exactly one result	Can contain 0, 1, or many outcomes
Probability (fair die)	$\frac{1}{6}$	Sum of probabilities of included outcomes, e.g. $\frac{3}{6} = \frac{1}{2}$
Notation	A single element of the sample space	A subset of the sample space

Why It Matters

Outcomes are the building blocks of all probability calculations. Every time you compute a probability — whether for games, statistics, genetics, or risk analysis — you start by identifying the possible outcomes. Understanding outcomes clearly is essential for correctly defining events and applying probability formulas in any course from introductory statistics to AP-level work.

Common Mistakes

Mistake: Confusing an outcome with an event. For instance, saying "rolling an even number" is an outcome.

Correction: "Rolling an even number" is an event made up of three outcomes: {2, 4, 6}. An outcome must be a single, indivisible result like "rolling a 4."

Mistake: Forgetting to count all outcomes in a compound experiment. For example, listing only 8 outcomes when flipping a coin and rolling a die.

Correction: Use the counting principle: multiply the number of outcomes for each part. A coin (2) times a die (6) gives

2 \times 6 = 12

total outcomes.

Related Terms

Experiment — The procedure that produces outcomes
Sample Space — The complete set of all possible outcomes
Event — A subset of outcomes from the sample space
Probability — Measures how likely an outcome or event is
Counting Principle — Finds total outcomes for compound experiments
Equally Likely Outcomes — Outcomes that all share the same probability