Free online probability calculator. Calculate simple probability, conditional probability (Bayes theorem), joint probability, permutations (nPr), combinations (nCr), and complementary probability. Instant results with formula explanations.
This probability calculator helps you compute various probability scenarios using fundamental statistical formulas. Whether you need to calculate the probability of a simple event, conditional probability using Bayes theorem, permutations, or combinations — this tool provides instant results with step-by-step explanations. All calculations are performed entirely in your browser for maximum privacy.
Simple probability is the likelihood of a single event occurring. It is calculated as the number of favorable outcomes divided by the total number of possible outcomes. For example, the probability of rolling a 4 on a fair die is 1/6 ≈ 0.167 or 16.7%.
Conditional probability is the probability of an event A occurring given that another event B has already occurred. It is calculated as P(A|B) = P(A∩B) / P(B), where P(A∩B) is the probability of both events occurring together.
Permutations (nPr) count arrangements where order matters. For example, ABC is different from BAC. Combinations (nCr) count selections where order does not matter. ABC and BAC are the same combination. The formulas are nPr = n!/(n-r)! and nCr = n!/(r!(n-r)!).
The complement of an event A is the event that A does not occur. The probability of the complement is P(A') = 1 - P(A). For example, if the probability of rain is 0.3, the probability of no rain is 0.7.