Probability Calculator
Calculate the probability of single events, complementary events, two independent events, and repeated trials — instantly with full result formats.
How to Use the Probability Calculator
Select Calculation Type: Choose from Single Event, Complementary, Two Events (AND/OR), or Repeated Trials using the mode selector tabs at the top of the tool.
Enter Favorable and Total Outcomes: Type the number of favorable outcomes and total possible outcomes for your event in the respective fields.
Fill Event B Values if Needed: For two-event calculations (AND / OR), also enter the favorable and total outcomes for Event B in the second block.
Click Calculate Probability: Press the Calculate button to see the probability as a decimal, percentage, fraction, and odds ratio instantly.
Review All Result Formats: Read the complete result including decimal probability, percentage, simplified fraction, odds for and odds against.
Clear and Recalculate: Use the Clear button to reset all fields and perform a new probability calculation from scratch.
Key Features
4 Calculation Modes
Covers single event, complementary, two independent events (AND/OR), and binomial repeated trials.
Multiple Result Formats
Results shown as decimal, percentage, simplified fraction, and odds for/against — all at once.
Visual Probability Bar
A visual bar instantly shows where your probability sits between impossible (0) and certain (1).
Smart Validation
Catches invalid inputs — empty fields, zero totals, favorable exceeding total — before calculation.
100% Private
All calculations happen in your browser. No data is stored or sent anywhere.
Instant Results
Get answers in milliseconds. No server round-trips, no waiting — pure client-side computation.
Probability Formulas Used in This Calculator
This calculator applies standard probability theory formulas established in classical mathematics. Here is exactly what each mode computes:
Practical Examples
Favorable outcomes: {5, 6} = 2 | Total outcomes: 6
P(A) = 2/6 = 0.3333 (33.33%)
P(Heart) = 13/52 = 0.25 | P(King) = 4/52 ≈ 0.0769 | P(Heart AND King) = 1/52 ≈ 0.0192
P(Heart OR King) = 0.25 + 0.0769 − 0.0192 = 0.3077 (30.77%)
p = 0.5, n = 10, k = 6
P(X=6) = C(10,6) × 0.5^6 × 0.5^4 = 210 × 0.015625 × 0.0625 = 0.2051 (20.51%)
P(Red) = 5/8 = 0.625 | P(Not Red) = 1 − 0.625 = 0.375 (37.5%)
What Is Probability?
Probability is the mathematical measure of how likely an event is to occur. It is expressed as a number between 0 and 1 — where 0 represents an impossible event and 1 represents a certain one. The field of probability theory forms the foundation of statistics, data science, machine learning, risk analysis, and decision-making across virtually every industry.
Classical probability, which this calculator uses, assumes all outcomes are equally likely. This applies perfectly to scenarios like coin flips, dice rolls, card draws, and lottery selections. More advanced probability models (Bayesian, conditional, continuous) build on this same foundation to handle real-world complexity.
Understanding probability is practically useful — from estimating the likelihood of rain, to evaluating business risk, to making informed decisions in games, exams, and everyday life. A solid grasp of basic probability gives you a measurable analytical advantage.
Probability in Your Language
Want a deeper understanding of probability concepts, real-world applications, and step-by-step examples?
Read the Full Probability Guide →Frequently Asked Questions
Is this probability calculator free to use?
Yes, this probability calculator is completely free to use with no registration, login, or hidden charges of any kind. Use it as often as you need.
What types of probability can this calculator compute?
This calculator handles single event probability, complementary probability (not happening), probability of two independent events both occurring (AND), probability of at least one event occurring (OR/Union), and probability in repeated trials using the binomial formula.
What is the basic probability formula?
The basic probability formula is P(A) = Number of Favorable Outcomes / Total Number of Possible Outcomes. The result is always between 0 and 1, where 0 means impossible and 1 means certain.
What is complementary probability?
Complementary probability is the probability that an event does NOT occur. If P(A) is the probability of an event happening, then P(A') = 1 − P(A). Together, P(A) + P(A') always equals exactly 1.
What is the difference between AND and OR probability?
AND probability (intersection) is the chance both events occur simultaneously: P(A∩B) = P(A) × P(B) for independent events. OR probability (union) is the chance at least one event occurs: P(A∪B) = P(A) + P(B) − P(A∩B).
What are independent events in probability?
Two events are independent if the occurrence of one does not affect the probability of the other. For example, rolling a die and flipping a coin are independent events. This calculator assumes independence for multi-event calculations.
How does the repeated trials probability work?
Repeated trials use the binomial probability formula: P(X=k) = C(n,k) × p^k × (1−p)^(n−k), where n is the number of trials, k is the desired number of successes, and p is the single-trial success probability.
What do odds for and odds against mean?
Odds for an event = Favorable outcomes : Unfavorable outcomes. Odds against = Unfavorable outcomes : Favorable outcomes. For example, if P(A) = 0.25, odds for are 1:3 and odds against are 3:1.
Can I use this for dice, cards, or coin problems?
Yes. For a fair coin, total outcomes = 2, favorable = 1 for heads. For a standard die, total = 6. For a card deck, total = 52. Enter the appropriate numbers for any scenario you need.
Is the data I enter stored anywhere?
No. All calculations run entirely in your browser. No data is sent to any server or stored anywhere. Your inputs are completely private.
Can probability ever be greater than 1 or less than 0?
No. Probability always ranges from 0 to 1 inclusive. A value of 0 means impossible; 1 means certain. Any value outside this range signals an error in the inputs, which this calculator validates and flags.
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