Calculate combinations (nCr), permutations (nPr), factorials, and basic event probability.
Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain), or as a percentage between 0% and 100%. The basic formula is: Probability = Number of favorable outcomes / Total number of possible outcomes. For example, the probability of rolling a 4 on a standard die is 1/6 = 0.1667 = 16.67%.
Enter the number of favorable outcomes and total possible outcomes for single event probability. For compound events, select whether the events are independent (one does not affect the other) or dependent, and whether you want the probability of both events occurring (AND) or at least one occurring (OR). The calculator handles combinations, permutations, and conditional probability.
Coin flips: P(heads) = 1/2. P(3 heads in a row) = (1/2)³ = 1/8 = 12.5%. Cards: P(drawing an ace) = 4/52 = 7.7%. P(drawing two aces) = (4/52) x (3/51) = 0.45%. Dice: P(rolling a 7 with two dice) = 6/36 = 16.7%. The Dice Roller and Coin Flip tools let you simulate these events.
Humans consistently misjudge probability in predictable ways. The conjunction fallacy leads people to rate specific scenarios as more likely than general ones (Linda the feminist bank teller). Base rate neglect causes overreaction to test results (a 99% accurate test still produces many false positives if the condition is rare). The availability heuristic makes vivid events (plane crashes) seem more probable than mundane ones (car accidents). Anchoring bias shifts probability estimates toward arbitrary starting points. Understanding these biases helps make better decisions. Practical probability facts: the odds of a royal flush in poker are 1 in 649,740. The odds of being struck by lightning in a given year are about 1 in 1,222,000. The odds of winning the Powerball jackpot are 1 in 292.2 million.