Introduction
This free probability calculator helps you find the chance that an event will or will not happen. Enter your values and get results as decimals, percentages, or fractions — with step-by-step solutions that show exactly how the math works.
The calculator has four modes. Single Event finds the probability of one outcome, like rolling a number on a die. Two-Event (Independent) calculates the probability of two events that do not affect each other, like flipping two coins. Dependent Events handles cases where one event changes the chance of another, using conditional probability and Bayes' theorem. Series of Events finds the combined probability of multiple independent events happening in a row, like winning several games in a streak.
Each mode includes clear formulas, Venn diagrams, and charts so you can see and understand the results. You can also use the quick-pick presets to load common examples — such as a die roll, card draw, or medical test — and start calculating right away.
How to Use Our Probability Calculator
Enter your known probability values or outcome counts, and this calculator will find the chance of events happening, not happening, or happening together. It gives results as decimals, percentages, and fractions, with full step-by-step solutions.
Quick Picks: Click any preset button at the top — like Die Roll, Two Coin Flips, Card Draw, Medical Test, or Win Streak — to load a common example and see how the calculator works right away.
Show Results as Fractions: Check this box to add a fraction column to every results table.
Single Event Tab
Input Method: Choose "Enter Probability" to type in a known probability, or choose "Enter Outcomes" to type in favorable and total outcomes instead.
Probability of Event P(E): Type the chance of your event as a decimal (like 0.25), a percent (like 25%), or a fraction (like 1/4). The value must be between 0 and 1. If you need to convert a decimal to a fraction first, try our decimal to fraction calculator.
Number of Favorable Outcomes n(E): Type how many outcomes count as a success. This must be a whole number that is zero or more.
Total Number of Possible Outcomes n(T): Type the total number of outcomes that could happen. This must be a whole number of at least 1, and it cannot be less than n(E).
Show Step-by-Step Solution: Check this box to see the math behind each result, broken into clear steps.
Show Venn Diagram: Check this box to see a visual diagram of the event and its complement inside the sample space.
Two-Event (Independent) Tab
Calculation Mode: Pick "Standard Calculator" to enter probabilities and get all results. Pick "Reverse Solver" to enter any two known values and let the calculator find the rest.
Probability of Event A — P(A): Type the chance that event A happens. Accepts a decimal, percent, or fraction between 0 and 1.
Probability of Event B — P(B): Type the chance that event B happens. Accepts a decimal, percent, or fraction between 0 and 1.
Mutually Exclusive Events: Check this box if events A and B can never happen at the same time. This sets P(A∩B) to zero. When checked, P(A) + P(B) cannot be more than 1.
Provide P(A∩B) Manually: Check this box if you know the exact probability that both A and B occur together, and you want to type it in yourself instead of having it calculated.
P(A∩B): If you checked the manual option, type the probability that both events happen at the same time. This value cannot be larger than the smaller of P(A) or P(B).
Reverse Solver: Fill in exactly two of the eight probability fields — such as P(A) and P(A∪B) — then click "Solve." The calculator will figure out the other six values using probability rules.
Dependent Events Tab
Target Probability: Use this dropdown to pick what you want to find, such as P(A|B), P(B|A), P(A∩B), P(A∪B), or other values.
Available Data: Use this dropdown to tell the calculator which values you already know. The input fields below will change based on your choice.
Input Fields: Type the known probability values that appear after you pick your target and data method. Each field accepts a decimal, percent, or fraction between 0 and 1. The calculator uses formulas like Bayes' theorem, the multiplication rule, and the addition rule to find your answer.
Series of Events Tab
Probability: For each event row, type the probability of that event succeeding on a single trial. Accepts a decimal, percent, or fraction between 0 and 1.
Times in a Row: For each event row, type how many times in a row that event must happen. This must be a whole number of at least 1. You can use our exponent calculator to verify individual power calculations.
Add Event: Click this button to add another event to the series. You can add up to 10 events. Click the trash icon on any row to remove it.
Show Step-by-Step Solution: Check this box to see the full formula and each step used to multiply the individual contributions into the combined probability.
What Is Probability?
Probability is the chance that something will happen. It is always a number between 0 and 1. A probability of 0 means the event will never happen. A probability of 1 means it will always happen. You can also write probability as a percent from 0% to 100% or as a fraction like 1/6.
How to Calculate Probability
The basic probability formula is simple. Divide the number of ways an event can happen by the total number of possible outcomes. For example, a standard die has 6 sides. The chance of rolling a 3 is 1 out of 6, or about 16.67%. For more complex dice scenarios — such as the probability of rolling a certain sum with multiple dice — use our dice probability calculator.
The complement of an event is the chance that the event does not happen. To find it, subtract the probability from 1. If the chance of rain is 0.3, the chance of no rain is 0.7.
Probability of Two or More Events
When you have two events, you can find the chance that both happen, that at least one happens, or that only one happens. The method depends on whether the events are independent or dependent.
Independent events do not affect each other. Flipping a coin does not change the next flip. For independent events, multiply their probabilities to find the chance both happen. Two coin flips that are both heads: 0.5 × 0.5 = 0.25, or 25%. When an event has only two outcomes like a coin flip and you want to know the probability of a certain number of successes across many trials, our binomial distribution calculator is the right tool.
Dependent events do affect each other. Drawing a card from a deck changes what is left for the next draw. For dependent events, you use conditional probability. The notation P(A|B) means "the probability of A given that B already happened." The formula is P(A|B) = P(A∩B) ÷ P(B). If you are drawing cards without replacement from a finite population, a hypergeometric calculator can handle those calculations directly.
Key Probability Rules
- Addition Rule: P(A or B) = P(A) + P(B) − P(A and B). This finds the chance that at least one of two events happens.
- Multiplication Rule: P(A and B) = P(A) × P(B|A). This finds the chance that both events happen.
- Complement Rule: P(not A) = 1 − P(A). This finds the chance an event does not happen.
- Bayes' Theorem: P(A|B) = [P(A) × P(B|A)] ÷ P(B). This lets you flip a conditional probability around when you know the reverse.
These rules work together with counting methods. If you need to find the total number of possible outcomes, a combination calculator helps when order does not matter, and a permutation calculator helps when order does matter. The number of favorable outcomes divided by the total gives you the probability.
Series of Independent Events
Sometimes you need the probability of the same thing happening many times in a row. If each event is independent, raise the probability to the power of how many times it repeats. For example, the chance of flipping heads 4 times in a row is 0.54 = 0.0625, or 6.25%. The more times you repeat a hard event, the smaller the combined probability gets. Sports bettors use this same principle when combining multiple bets — our parlay calculator applies this logic to calculate combined betting odds.
If you want to know the average outcome rather than the combined probability of a series, our EV calculator can help you find the expected value of repeated events.
Mutually Exclusive Events
Two events are mutually exclusive if they cannot both happen at the same time. Rolling a 2 and rolling a 5 on one die are mutually exclusive. When events are mutually exclusive, P(A and B) = 0, and the addition rule becomes simply P(A or B) = P(A) + P(B). You can also express mutually exclusive probabilities as odds, which compare the chance of an event happening to the chance of it not happening.