Probability Calculator: Odds & Likelihood
Calculate probability, expected value, and permutations for dice, cards, events, and statistical experiments.
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Probability Calculator: Odds & Likelihood A probability calculator computes the likelihood of events — single events, combined events, conditional probabilities, combinations, and permutations — using standard probability formulas so you can quantify risk, evaluate game odds, design experiments, and understand statistical claims without manual calculation. The NIST/SEMATECH e-Handbook of Statistical Methods provides authoritative reference material on probability distributions and statistical calculations. --- What Is Probability? Probability quantifies uncertainty. For any event, it ranges from 0 (impossible) to 1 (certain). Most practical probabilities fall somewhere between. Key definitions: | Term | Definition | Example | |------|-----------|---------| | Probability | Likelihood of an…
Frequently Asked Questions
What is probability?
Probability is a number between 0 and 1 expressing the likelihood of an event occurring. P=0 means impossible, P=1 means certain, P=0.5 means equally likely to happen or not. It can be expressed as a fraction (1/6), decimal (0.1667), or percentage (16.67%).
How do I calculate the probability of two events?
For independent events, multiply their individual probabilities: P(A and B) = P(A) × P(B). For the probability that at least one occurs: P(A or B) = P(A) + P(B) - P(A and B). A probability calculator automates these formulas for common scenarios.
What is conditional probability?
Conditional probability P(A|B) is the probability of event A occurring given that B has already occurred. Formula: P(A|B) = P(A and B) / P(B). Example: the probability of drawing a king given that you've already drawn a face card.
How do I calculate combinations and permutations?
Combinations C(n,r) = n! / (r!(n-r)!) count ways to choose r items from n without regard to order. Permutations P(n,r) = n! / (n-r)! count ordered arrangements. A probability calculator handles the factorial arithmetic automatically.
What is expected value?
Expected value (E[X]) is the average outcome over many trials, calculated as the sum of each possible outcome multiplied by its probability. In a fair d6 roll, E[X] = (1+2+3+4+5+6)/6 = 3.5. It represents the long-run average, not necessarily a value that can actually occur.
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