Probability Calculator
Calculate probabilities for single and multiple events. Supports combinations, permutations, and conditional probability.
About Probability Calculator
A probability calculator computes the likelihood of events occurring, supporting calculations for single events, multiple events, combinations, permutations, and conditional probability. Probability theory is the mathematical foundation of statistics, gambling, insurance, risk assessment, and machine learning. Understanding probability helps make informed decisions under uncertainty, from evaluating weather forecasts to assessing business risks.
How to Use
Choose the calculation type: basic probability (P = favorable outcomes / total outcomes), complement (1 - P), multiple independent events (P(A and B) = P(A) × P(B)), mutually exclusive events (P(A or B) = P(A) + P(B)), combinations (nCr), or permutations (nPr). Enter your values and the calculator shows the result as both a fraction and a percentage.
Formula / Key Equations
Basic: P(A) = favorable outcomes / total outcomes. Complement: P(not A) = 1 - P(A). Independent events: P(A and B) = P(A) × P(B). Mutually exclusive: P(A or B) = P(A) + P(B). Combinations: nCr = n! / (r!(n-r)!). Permutations: nPr = n! / (n-r)!.
Common Use Cases
Calculating lottery odds and game probabilities. Assessing risk in business decisions and insurance. Determining the likelihood of medical test results (sensitivity/specificity). Computing probabilities for card games and dice rolls. Understanding statistical significance in research. Estimating failure rates in engineering reliability analysis.
Limitations
The calculator assumes fair random processes unless specified. It handles independent events but not dependent events with complex conditional probability chains. For continuous probability distributions (normal, binomial, Poisson), use specialized statistical tools. Very large factorial calculations may be limited by computational precision.
Frequently Asked Questions
What is the difference between permutations and combinations?
Permutations consider order (ABC is different from BAC), while combinations do not (ABC and BAC are the same). Use permutations when arrangement matters (seating arrangements, passwords) and combinations when only the group matters (picking a team from a roster).
What does independent vs mutually exclusive mean?
Independent events do not affect each other (coin flips). Mutually exclusive events cannot happen at the same time (rolling a 1 and a 6 on one die). Independent events can happen together; mutually exclusive events cannot.
How do I calculate conditional probability?
Conditional probability P(A|B) is the probability of A given that B has occurred: P(A|B) = P(A and B) / P(B). For example, the probability of drawing a king from a deck given that you drew a face card is 4/12 = 1/3.
What are the odds of winning the lottery?
It depends on the lottery format. For a typical 6/49 lottery: the number of combinations is C(49,6) = 13,983,816, so the probability is approximately 1 in 14 million (0.00000715%). Use our combinations calculator to find odds for any lottery format.
Can this calculator handle the birthday problem?
The birthday problem asks: in a group of n people, what is the probability that at least two share a birthday? For 23 people, the probability is about 50.7%. This is a classic probability puzzle because the answer is much higher than most people intuit. You can work through it step by step using our calculator.
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