BrainyCalculators
Login
Advertisement

🎲 Probability Calculator

Calculate probability for single events, combined events (AND/OR), and conditional probability. Results shown as fraction, decimal, and percentage. Complement (NOT event) always included.

Key Probability Formulas

Basic Probability
P(A) = Favorable outcomes / Total outcomes
Complement Rule
P(not A) = 1 − P(A)
Multiplication Rule (Independent)
P(A and B) = P(A) × P(B)
Addition Rule (General)
P(A or B) = P(A) + P(B) − P(A and B)
Conditional Probability
P(A|B) = P(A ∩ B) / P(B)

How to Use This Calculator

  1. 1
    Choose a Calculation Type
    Select Single Event for basic probability, Two Events to combine probabilities with AND/OR, or Conditional for P(A|B).
  2. 2
    Enter Your Values
    For single events, enter favorable and total outcomes. For two events, enter P(A) and P(B) as decimals between 0 and 1.
  3. 3
    Select Event Relationship
    For two events, choose Independent (events do not affect each other) or Mutually Exclusive (events cannot both occur).
  4. 4
    Read the Results
    Results show probability as a decimal, percentage, and fraction. The complement (NOT event) is always included.

Worked Example

Rolling a standard six-sided die — what is the probability of getting an even number?

Even numbers on a die: {2, 4, 6} → Favorable = 3
Total outcomes = 6
P(even) = 3 / 6 = 0.5 = 50%
P(not even) = 1 − 0.5 = 0.5 = 50%

Frequently Asked Questions

Probability is a number between 0 and 1 that measures how likely an event is to occur. A probability of 0 means the event is impossible; 1 means it is certain. It is calculated as the number of favorable outcomes divided by the total number of possible outcomes, assuming all outcomes are equally likely.

Two events are mutually exclusive (or disjoint) if they cannot both occur at the same time. For example, a coin flip cannot be both heads and tails. For mutually exclusive events, P(A and B) = 0 and P(A or B) = P(A) + P(B).

Two events are independent if the occurrence of one does not affect the probability of the other. For example, rolling a die twice — the result of the first roll does not affect the second. For independent events, P(A and B) = P(A) × P(B).

Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. It is calculated as P(A|B) = P(A ∩ B) / P(B). This is fundamental to Bayes's theorem and is used widely in statistics, medicine, and machine learning.

Related Calculators

🎯 Statistics

Binomial Distribution Calculator

Calculate binomial probability P(X=k), cumulative probabilities, mean, and variance.

Calculate now
P Statistics

Permutation Calculator

Calculate the number of permutations P(n,r) — ordered arrangements.

Calculate now
C Statistics

Combination Calculator

Calculate the number of combinations C(n,r) — unordered selections.

Calculate now