Quickly compute single-event probabilities, independent event combinations (AND/OR), and binomial probabilities with this easy-to-use Probability Calculator. Enter the values you know and get precise decimal and percentage results in seconds.
What the Probability Calculator Can Do
The Probability Calculator helps you estimate the likelihood of outcomes across common scenarios. Whether you are drawing cards, rolling dice, planning A/B tests, or modeling success rates in repeated trials, this tool delivers accurate calculations tailored to your inputs. It supports three major use cases:
- Single event probability: Compute favorable outcomes divided by total outcomes.
- Independent events (AND/OR): Combine probabilities using standard rules for independent events.
- Binomial probability: Model the probability of a given number of successes across n independent trials with success probability p.
How to Use the Calculator
1) Single Event Probability
Choose "Single event probability" and enter the number of favorable outcomes and total possible outcomes. For example, drawing a heart from a standard deck gives 13 favorable outcomes out of 52 total outcomes. The calculator returns the probability as a decimal and a percentage. You’ll also see the fraction simplified for clarity.
2) Independent Events: AND and OR
For independent events, enter P(A) and P(B) as decimals between 0 and 1. The calculator applies the standard rules:
- AND (A and B): P(A and B) = P(A) × P(B)
- OR (A or B): P(A or B) = P(A) + P(B) ? P(A) × P(B)
These formulas assume independence. For dependent events, you would need conditional probabilities, which are outside the current scope of this tool.
3) Binomial Probability
Use the binomial options when you run repeated, identical, independent trials with a constant success probability p (for example, conversions per visit, hits per at-bat, or test pass rates). Select the exact outcome you need:
- Exact k successes: The probability of getting exactly k successes in n trials.
- At least k successes: The probability of getting k or more successes.
- At most k successes: The probability of getting k or fewer successes.
The calculator uses the binomial formula with combinations to produce precise results: it multiplies the number of ways to achieve k successes by the probability of each such outcome.
Why This Calculator Is Useful
Accurate probability estimates support better decisions in marketing, product testing, quality control, gaming, and education. With clear inputs and instant results, this calculator reduces manual errors and reveals how likely events really are. You can also set decimal precision to match your reporting standards.
Tips for Accurate Results
- Enter probabilities as decimals (for example, 0.2 for 20%).
- Use the correct mode: single event counts, independent event probabilities, or binomial trials.
- Confirm independence assumptions when selecting AND/OR for events.
- For binomial problems, verify that trials are identical and independent, with a constant success probability.
- Adjust decimal places to balance readability and precision.
Example Scenarios
Single Event
What is the probability of rolling an even number on a fair six-sided die? Favorable outcomes = 3 (2, 4, 6), total outcomes = 6, so the probability is 3/6 = 0.5 or 50%.
Independent AND
If P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.3 × 0.5 = 0.15, or 15%.
Binomial Exact
What is the probability of getting exactly 3 heads in 10 fair coin flips? Here, n = 10, k = 3, p = 0.5. The calculator applies the binomial formula to give the precise result.
From Classroom to Real-World Decisions
Beyond homework and exams, probability underpins decisions in experimentation, forecasting, and risk management. Use this Probability Calculator to translate assumptions and data into clear, defensible numbers you can act on.