An outcome is one possible result of a chance experiment, such as rolling a 4 on a number cube or getting tails on a coin flip. The set of all outcomes is the sample space, and a group of outcomes is an event. When outcomes are equally likely, each one has probability 1 divided by the number of outcomes.
In Spanish
resultado
Also called
possible outcome, result, elementary event, sample point
An outcome is one possible result. Count outcomes carefully, and check whether they are equally likely before you divide.
Formal definition and notation
For a chance process (an experiment whose result is not known in advance), an outcome is a single possible result, one element of the sample space S. Exactly one outcome happens on each trial. In a uniform probability model every outcome has the same probability, 1n when S has n outcomes; in other models, such as a spinner with unequal sections, outcomes can have different probabilities, which still add to 1.
one outcome of a two-part experiment, written as an ordered pair
Key facts
Each trial produces exactly one outcome; two outcomes of the same trial cannot both happen.
Outcomes are the building blocks: an event is a set of outcomes, and the sample space is the set of all of them.
Equally likely outcomes: P(one outcome) = 1n. A number cube gives 16 per face.
Not all outcomes are equally likely. A spinner with a bigger red part lands on red more often.
For two-step experiments, write outcomes as ordered pairs: (H, 3) and (T, 3) are different outcomes.
The probabilities of all the outcomes always add to 1.
Try it: outcomes that are not equally likely
Interactive
This spinner has 3 outcomes, but C covers half the circle. Spin 100 or 1,000 times: C comes up about twice as often as A or B.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Outcome examples, step by step
Example 1: List the outcomes
Warm-up
A bag holds one red, one green and one white marble. You draw one marble. List the outcomes and give the probability of each.
The possible results are red, green and white: 3 outcomes.
Each marble is equally likely to be drawn, so each outcome has probability 13.
Answer: The outcomes are red, green and white, each with probability 1/3.
Example 2: Outcomes of a two-step experiment
Core
You flip a coin and then spin a spinner with sections 1, 2 and 3 of equal size. How many outcomes are there, and what is the probability of the outcome (T, 2)?
A spinner is split into a red section of 180 degrees, a blue section of 120 degrees and a yellow section of 60 degrees. What is the probability of the outcome blue?
The outcomes are red, blue and yellow, but the sections are different sizes, so they are not equally likely.
Use the angle: P(blue) = 120360.
120360 = 13.
Answer: P(blue) = 1/3, not 1/3 because there are 3 colors, but because blue covers a third of the circle.
Common mistakes
✗ MistakeAssuming every outcome is equally likely: the spinner above has 3 colors, so P(red) = 13.
✓ InsteadRed covers 180 of 360 degrees: P(red) = 12.
1n works only for equally likely outcomes. Check the sizes of the sections.
✗ MistakeCounting (H, 3) and (3, H) as two outcomes, or listing (H, 3) twice.
✓ InsteadList each outcome once, in a fixed order (coin first, spinner second).
A careless list double-counts or misses outcomes, which changes every probability.
✗ MistakeCalling “an even number” an outcome of rolling a cube.
✓ Instead“Even” is an event made of the outcomes 2, 4 and 6.
An outcome is a single result; an event can contain several outcomes.
The sample space is the whole list of outcomes, such as {1, 2, 3, 4, 5, 6} for a number cube. One outcome is one member of that list.
Quick check: 3 questions
Question 1 of 3
How many outcomes are there when you roll one number cube?
Show answer and explanation
Answer: C. The faces 1, 2, 3, 4, 5 and 6 are the 6 outcomes. 1 is a single result, 3 counts only the even faces, and 12 is for two dice sums or coin-and-cube pairs.
Question 2 of 3
Which of these is an outcome, not an event with several outcomes, when you roll a number cube?
Show answer and explanation
Answer: A. “Rolling a 4” is one single result. The other three describe groups of outcomes: {2, 4, 6}, {3, 4, 5, 6} and {1, 6}.
Question 3 of 3
A coin is flipped and a number cube is rolled. How many outcomes are possible?
Show answer and explanation
Answer: D. Each of the 2 coin results pairs with each of the 6 cube results: 2 × 6 = 12. 8 adds instead of multiplying, and 6 and 2 count only one part.
Outcome: frequently asked questions
What is the difference between an outcome and an event?
An outcome is one possible result, such as rolling a 3. An event is any set of outcomes, such as “rolling an odd number,” which contains 1, 3 and 5. An event can contain just one outcome, so “rolling a 3” is also an event, a simple one.
Are all outcomes equally likely?
No. Coins, number cubes and spinners with equal sections give equally likely outcomes. A spinner with a bigger section, a weighted die, or the weather tomorrow does not. When outcomes are not equally likely, you cannot just divide by the number of outcomes; use the sizes of the sections or data from many trials.
Sample SpaceThe sample space of a chance experiment is the set of all its possible outcomes, usually written S. For one coin flip, S = {H, T}; for one number cube, S = {1, 2, 3, 4, 5, 6}. Organized lists, tables and tree diagrams help you write it out, and the probabilities of all its outcomes add to 1.Probability · Grade 7, Grade 8, StatisticsEventAn event is a set of one or more outcomes of a chance experiment, such as “rolling an even number” on a number cube. It is part of the sample space. When outcomes are equally likely, the probability of an event is the number of outcomes in it divided by the number of outcomes in the sample space.Probability · Grade 7, Grade 8, StatisticsProbabilityProbability measures how likely an event is, from 0 for impossible to 1 for certain. For equally likely outcomes it is the number of favorable outcomes divided by the total number of outcomes: for a fair coin, the probability of heads is 12. Probabilities can be written as fractions, decimals or percents.Probability · Grade 6, Grade 7, Grade 8NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Ordered PairAn ordered pair is two numbers written to locate a point on the coordinate plane. It is written as (x, y): the x-value comes first, and the y-value comes second. From the origin, move x units across, then y units up or down. The order matters: (2, 5) and (5, 2) are different points.Geometry · Grade 5, Grade 6, Grade 7DegreeA degree is the standard unit for measuring an angle, written with the symbol °. One degree is 1360 of a full turn, so a full turn is 360°, a straight angle is 180° and a right angle is 90°. An angle that turns through 25 one-degree angles measures 25°.Geometry · Grade 4, Grade 5, Grade 7CircleA circle is the set of all points in a flat plane that are the same distance from one fixed point, the center. That distance is the radius. A segment through the center from edge to edge is the diameter, twice the radius. The distance around is the circumference, 2π r, and the area inside is π r2.Geometry · Kindergarten, Grade 1, Grade 7Even NumberAn even number is an integer that can be divided by 2 with no remainder, so it can be split into two equal groups or into pairs. Even numbers end in 0, 2, 4, 6 or 8, such as 14, 236 and −10. Zero is even. Every even number can be written as 2n for some integer n.Number System · Grade 2, Grade 3, Grade 4Odd NumberAn odd number is a whole number that cannot be split into two equal groups: dividing it by 2 always leaves a remainder of 1. Odd numbers end in 1, 3, 5, 7 or 9, such as 7, 23 and 409. Every odd number can be written as 2k + 1, one more than a multiple of 2.Number System · Grade 2, Grade 3, Grade 4DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6Compound EventA compound event is an event that combines two or more simple events, such as flipping heads and rolling a 6, or drawing a red card or a king. Find its probability by counting outcomes in a list, table or tree diagram, or with rules such as P(A and B) = P(A) × P(B) for independent events.Probability · Grade 7, Grade 8, StatisticsIndependent EventsIndependent events are two events where the outcome of one does not change the probability of the other. Flipping heads on a coin does not affect rolling a 5 on a die. For independent events, multiply: P(A and B) = P(A) × P(B), so P(heads and 5) = 12 × 16 = 112.Probability · Grade 7, Algebra 1, Algebra 2Relative FrequencyRelative frequency is how often a value or event occurs compared with the total number of observations: frequency ÷ total. It can be a fraction, a decimal or a percent. If 12 of 40 students choose apples, the relative frequency of apples is 1240 = 0.3, or 30%. All the relative frequencies in a table add to 1.Statistics · Grade 7, Grade 8, StatisticsPermutationA permutation is an arrangement of objects in a specific order, so ABC and CBA count as different. The number of ways to arrange r objects chosen from n different objects is P(n, r) = n!(n − r)!. For example, picking a president and vice president from 5 people gives 5 × 4 = 20 permutations.Probability · Algebra 2, Precalculus, Statistics