Probability Calculator

Mutually exclusive events cannot happen at the same time (e.g., rolling a 3 and a 4 on a single die roll; P(A and B) = 0). Independent events are events where the occurrence of one does not affect the occurrence of the other (e.g., rolling a 3 on a die, and flipping heads on a coin; P(A and B) = P(A) × P(B)).

If the odds in favor of an event are 'A to B' (written as A:B), the probability is calculated as P = A / (A + B). For example, odds of 1:3 in favor represent a probability of 1 / (1 + 3) = 1/4, or 25%.

Conditional probability measures the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), read as 'the probability of A given B'. The formula is P(A|B) = P(A and B) / P(B).

Probability represents the ratio of desired outcomes to the total possible outcomes. Since the number of desired outcomes can never be negative (minimum 0) and can never exceed the total possible outcomes (maximum equal to total), the ratio is mathematically bound between 0 (impossible event) and 1 (certain event) or 0% and 100%.

The Law of Large Numbers states that as you repeat an experiment or trial more times (like flipping a coin), the experimental probability (observed ratio of heads) will get closer and closer to the theoretical probability (exactly 50%). It does not guarantee short-term streaks will correct themselves, but it governs long-term trends.