Probability Terms

Probability basics 5

• EventAn 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.Grade 7, Grade 8, Statistics
• OddsOdds compare the number of ways an event can happen with the number of ways it cannot, written as a ratio such as 3 to 2 or 3:2. Odds in favor are favorable : unfavorable, and odds against are the reverse. Probability instead divides favorable outcomes by all outcomes, so 3:2 odds mean a probability of 3/5.Grade 7, Statistics
• OutcomeAn 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.Grade 7, Grade 8, Statistics
• ProbabilityProbability 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 1/2. Probabilities can be written as fractions, decimals or percents.Grade 6, Grade 7, Grade 8
• 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.Grade 7, Grade 8, Statistics

Compound events 5

• Compound 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.Grade 7, Grade 8, Statistics
• Conditional ProbabilityConditional probability is the probability that an event happens given that another event has already happened. It is written P(A ∣ B), read "the probability of A given B", and found by P(A ∣ B) = (P(A and B))/(P(B)). Knowing B shrinks the possible outcomes to only those in B.Algebra 2, Statistics
• Dependent EventsDependent events are two events where the outcome of the first changes the probability of the second. Drawing two cards without putting the first one back is the classic example. For dependent events, P(A and B) = P(A) × P(B ∣ A), where P(B ∣ A) is the probability of B once A has happened.Grade 7, Algebra 2, Statistics
• Independent 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) = 1/2 × 1/6 = 1/12.Grade 7, Algebra 1, Algebra 2
• Mutually Exclusive EventsMutually exclusive events are events that cannot happen at the same time, so P(A and B) = 0. Rolling a 2 and rolling a 5 on one roll of a number cube are mutually exclusive. For such events the addition rule is simple: P(A or B) = P(A) + P(B).Grade 7, Algebra 2, Statistics

Counting 3

• CombinationA combination is a selection of items from a group in which the order does not matter. Picking Ana, Ben and Cy for a team is the same combination as Cy, Ana and Ben. The number of ways to choose r items from n is C(n, r) = (n!)/(r!(n − r)!); for example, C(5, 2) = 10.Algebra 2, Precalculus, Statistics
• FactorialThe factorial of a whole number n, written n!, is the product of all the whole numbers from n down to 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. It counts the ways to arrange n different objects in a row. By agreement, 0! = 1.Algebra 2, Precalculus, Statistics
• PermutationA 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.Algebra 2, Precalculus, Statistics

Sets and Venn diagrams 3

• SetA set is a well-defined collection of distinct objects, called elements or members. Sets are written with curly braces and named with capital letters, as in A = {2, 4, 6}. Order does not matter and repeated items count once, so {1, 2, 3} and {3, 1, 2} are the same set.Grade 6, Algebra 1, Statistics
• SubsetA subset is a set whose elements all belong to another set. If every element of A is also in B, then A is a subset of B, written A ⊆ B. Every set is a subset of itself, the empty set is a subset of every set, and a set with n elements has 2^n subsets.Algebra 1, Statistics
• Venn DiagramA Venn diagram is a picture that uses overlapping circles inside a rectangle to show how groups, or sets, are related. Each circle is a set, the overlap holds items in both sets, and the rectangle holds everything being considered. Venn diagrams make it easy to count "and", "or" and "not" cases and to find probabilities.Grade 7, Algebra 2, Statistics

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Updated November 2026·Reviewed by the Effortless Math team