Probability Calculator
Calculate the probability of a single event from favorable and total outcomes, or combine two independent events to find P(A and B), P(A or B), the complement, and more.
- 01Find single event probability instantly: favorable outcomes ÷ total outcomes.
- 02Combine two independent events for P(A and B), P(A or B), and P(neither).
- 03See probability as a decimal, a percentage, and as odds.
- 04Get the complement P(A') and P(exactly one) in a clear results grid.
- 05100% free and private — every calculation runs in your browser.
Probability Calculator
The number of outcomes that count as success.
The total number of equally likely possible outcomes.
Probability P(E)
0.25
P(E) = f ÷ t, a value between 0 and 1
As a percentage
25%
Probability × 100
Odds in favor
13 : 39
Favorable : unfavorable (f : t − f)
Favorable (f)
13
Total (t)
52
Complement P(E')
0.75
Complement %
75%
Why Use This Probability Calculator
Single Event Probability
Enter the favorable outcomes and the total number of equally likely outcomes, and the calculator returns the single event probability as P(E) = f ÷ t — instantly, with the result shown as a decimal, a percentage, and as odds in favor.
Two Independent Events
Provide P(A) and P(B) and get every combined probability at once: P(A and B), P(A or B), P(neither), and P(exactly one). It is the fastest way to calculate the probability of two independent events without working through each formula by hand.
Union, Intersection and Complement
See the intersection P(A ∩ B), the union P(A ∪ B), and the complement P(A') = 1 − P(A) side by side. The results grid makes the relationship between AND, OR, and NOT probabilities easy to read and verify.
Decimal, Percentage and Odds
Every probability is shown three ways — as a decimal between 0 and 1, as a percentage, and (for single events) as odds. Switch between formats without re-running the calculation or doing extra arithmetic.
Instant and Private
Everything runs entirely in your browser with no server round-trips. Your inputs never leave your device, results appear instantly, and there is no signup or installation required to use the probability calculator.
Free with No Limits
Calculate as many probabilities as you need — no daily limits, no account, and no paywall. The full probability calculator for single events and two independent events is completely free.
What Is Probability?
Probability is a measure of how likely an event is to happen, expressed as a number between 0 (impossible) and 1 (certain). For equally likely outcomes, the probability of an event equals the number of favorable outcomes divided by the total number of possible outcomes. Probability is the foundation of statistics, risk analysis, games of chance, machine learning, and everyday decision-making.
Whether you are a student learning how to calculate probability, a teacher building examples, or an analyst weighing combined risks, this probability calculator gives instant, accurate results for single events and two independent events.
- Single Event Probability
- The probability of a single event is P(E) = favorable outcomes ÷ total outcomes. For example, the probability of drawing a heart from a standard 52-card deck is 13 ÷ 52 = 0.25, or 25%. The complement, P(E') = 1 − P(E), is the probability the event does not happen.
- Independent Events: P(A and B)
- Two events are independent when one does not affect the other. For independent events, the probability that both occur is the product P(A and B) = P(A) · P(B). This multiplication rule is how the calculator finds the intersection P(A ∩ B) of two independent events.
- P(A or B) and the Addition Rule
- The probability that at least one of two events occurs is P(A or B) = P(A) + P(B) − P(A and B). Subtracting the overlap P(A ∩ B) avoids double-counting outcomes that belong to both events, giving the correct union P(A ∪ B).
- Conditional vs Independent Events
- Conditional probability P(A given B) describes how likely A is once B is known to have occurred, written P(A | B) = P(A ∩ B) ÷ P(B). When events are independent, knowing B changes nothing, so P(A | B) = P(A) and the simple multiplication rule applies.
How to Use the Probability Calculator
- 01
Choose a mode
Pick the Single event tab to find the probability of one event, or the Two events tab to combine two independent events. The calculator loads with sensible example values so you can see a result straight away.
- 02
Enter your numbers
For a single event, type the favorable outcomes (f) and the total outcomes (t). For two events, enter P(A) and P(B) as probabilities between 0 and 1, for example 0.5 and 0.2.
- 03
Click Calculate
Press the Calculate button. The tool validates your inputs — total cannot be zero and probabilities must be between 0 and 1 — then computes the result instantly in your browser.
- 04
Read the results
For a single event you get the probability, percentage, odds, and complement. For two events you get P(A and B), P(A or B), P(neither), P(exactly one), and the complements P(A') and P(B') in a clear results grid.
Tips for Calculating Probability
Keep Probabilities Between 0 and 1
Every probability is a number from 0 (impossible) to 1 (certain). If you are working in percentages, divide by 100 first — for example, enter 25% as 0.25 in the two-events mode.
Check Independence Before Multiplying
The rule P(A and B) = P(A) · P(B) only holds when the two events are independent. If one event changes the probability of the other, you need conditional probability, P(A | B), instead of simple multiplication.
Subtract the Overlap for P(A or B)
For the union of two events, use P(A or B) = P(A) + P(B) − P(A and B). Forgetting to subtract the intersection double-counts the overlap and overstates the probability.
Use the Complement Shortcut
Sometimes 'at least one' is easier to find as 1 − P(neither). The complement rule P(A') = 1 − P(A) can turn a hard calculation into a simple one, especially with several independent events.
Count Outcomes Carefully
For single events, make sure the total counts every equally likely outcome and that favorable is a subset of it (0 ≤ f ≤ t). Miscounting the sample space is the most common source of probability errors.
Convert to the Right Format
Decimals are best for further calculation, percentages communicate likelihood clearly, and odds are common in betting. This calculator shows all of them so you can report probability in the form your audience expects.
Probability Formulas and Definitions
Definition of probability
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). For equally likely outcomes, the probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
What the probability rules tell you
- Single event: P(E) = favorable ÷ total, always between 0 and 1.
- Complement: P(E') = 1 − P(E), the chance the event does not happen.
- Multiplication rule (independent): P(A and B) = P(A) · P(B).
- Addition rule: P(A or B) = P(A) + P(B) − P(A and B).
Independent vs conditional events
Two events are independent when one does not affect the other, so the simple multiplication rule applies. If one event changes the probability of the other, use conditional probability P(A | B) = P(A ∩ B) ÷ P(B) instead.
Key Probability Formulas
Single event probability
P(E) = f ÷ t
Example: drawing a heart = 13 ÷ 52 = 0.25 (25%).
Complement
P(E') = 1 − P(E)
If P(E) = 0.25, then P(E') = 0.75.
Intersection — P(A and B)
P(A ∩ B) = P(A) · P(B)
Independent events: 0.5 × 0.2 = 0.1.
Union — P(A or B)
P(A ∪ B) = P(A) + P(B) − P(A) · P(B)
0.5 + 0.2 − 0.1 = 0.6.
Neither event
P(neither) = (1 − P(A))(1 − P(B))
0.5 × 0.8 = 0.4 for the example above.
Exactly one event
P(exactly one) = P(A ∪ B) − P(A ∩ B)
0.6 − 0.1 = 0.5 for the example above.
Probability Calculator FAQ
Q01How do I calculate probability?
For a single event with equally likely outcomes, divide the number of favorable outcomes by the total number of possible outcomes: P(E) = f ÷ t. For example, rolling a 4 on a six-sided die is 1 ÷ 6 ≈ 0.167, or about 16.7%. This calculator does the division for you and also shows the result as a percentage and as odds.
Q02How do I find the probability of two events?
It depends on what you want. For two independent events, the probability that both happen is P(A and B) = P(A) · P(B), and the probability that at least one happens is P(A or B) = P(A) + P(B) − P(A and B). Enter P(A) and P(B) in the Two events tab and the calculator returns both, plus P(neither) and P(exactly one).
Q03What is P(A and B) for independent events?
For independent events, P(A and B) — the intersection P(A ∩ B) — is the product of the two probabilities: P(A and B) = P(A) · P(B). For example, if P(A) = 0.5 and P(B) = 0.2, then P(A and B) = 0.5 × 0.2 = 0.1. Multiplication only applies when the events do not affect each other.
Q04What is P(A or B)?
P(A or B) is the probability that at least one of the two events occurs, the union P(A ∪ B). Using the addition rule, P(A or B) = P(A) + P(B) − P(A and B). The intersection is subtracted so outcomes in both events are not counted twice. With P(A) = 0.5 and P(B) = 0.2, P(A or B) = 0.5 + 0.2 − 0.1 = 0.6.
Q05What is the difference between independent and conditional probability?
Events are independent when one does not change the probability of the other, so P(A and B) = P(A) · P(B). Conditional probability, P(A | B) = P(A ∩ B) ÷ P(B), measures how likely A is given that B has happened. For independent events, P(A | B) = P(A). This calculator's two-events mode assumes independence.
Q06What is the complement of an event?
The complement of an event E is everything in which E does not happen, written E'. Its probability is P(E') = 1 − P(E). Because an event either happens or it does not, P(E) + P(E') = 1. The calculator shows the complement for single events and P(A'), P(B'), and P(neither) for two events.
Q07Can probability be greater than 1 or negative?
No. A valid probability is always between 0 and 1 inclusive: 0 means impossible and 1 means certain. If you enter a probability outside this range, or favorable outcomes greater than the total, the calculator flags it so you can correct the input.
Q08Is this probability calculator free and private?
Yes. It is completely free with no signup, no limits, and no premium tier. All calculations run in your browser using JavaScript, so your numbers are never uploaded or stored anywhere.