Understanding Probability
Probability measures how likely an event is to occur, expressed as a number between 0 and 1, where 0 means impossible and 1 means certain. This probability calculator helps you compute the chance of multiple events happening together, the chance that at least one event occurs, and binomial probabilities for repeated trials.
Independent vs. Dependent Events
Two events are independent when the outcome of one does not affect the outcome of the other, such as flipping a coin twice or rolling two dice. For independent events, the probability that both occur is the product of their individual probabilities. Dependent events are different because the first outcome changes the probability of the second, as when drawing cards from a deck without replacement.
Combining Events with AND and OR
The probability of two independent events both occurring is calculated by multiplying their probabilities together. The probability that at least one of several events occurs is found by subtracting the probability that none occur from one. These two rules cover most everyday probability questions, from game strategy to risk assessment. This calculator assumes the events you enter are independent.
Binomial Probability
Binomial probability applies when you repeat the same trial several times and want to know the chance of getting exactly a certain number of successes. For example, if you flip a fair coin 10 times, the binomial formula tells you the probability of getting exactly 5 heads. It uses the number of trials, the per-trial success probability, and the target number of successes.
If you need random outcomes for a simulation or game, try our random number generator. It produces fair random numbers you can use to model events and test probabilities in practice.