Probability Calculator

Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% to 100%). A probability of 0 means the event is impossible, 1 means it is certain, and 0.5 means it has an equal chance of occurring or not occurring. Probability is fundamental to statistics, gambling, risk assessment, and decision-making.

Basic probability is calculated using the formula: P(Event) = Number of Favorable Outcomes / Total Number of Possible Outcomes. For example, the probability of rolling a 3 on a six-sided die is 1/6, because there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes (1, 2, 3, 4, 5, or 6).

AND probability (multiplication rule) calculates the chance that multiple events ALL occur: P(A AND B) = P(A) * P(B) for independent events. OR probability (addition rule) calculates the chance that AT LEAST ONE event occurs: P(A OR B) = P(A) + P(B) - P(A AND B). For example, rolling a 6 AND flipping heads is (1/6) * (1/2) = 1/12, while rolling a 6 OR flipping heads is 1/6 + 1/2 - 1/12 = 7/12.

Conditional probability is the probability of an event A occurring given that another event B has already occurred, denoted as P(A|B). The formula is: P(A|B) = P(A AND B) / P(B). For example, if the probability of rain is 30% and the probability of rain AND cold weather is 15%, then the probability of rain given cold weather is 15% / P(cold) = P(rain|cold).

The complement of an event is the probability that the event does NOT occur, denoted as P(A') or P(NOT A). It equals 1 - P(A). For example, if the probability of winning a game is 0.3 (30%), the probability of not winning is 1 - 0.3 = 0.7 (70%). The probabilities of an event and its complement always sum to 1.

To convert probability (p) to percentage, multiply by 100. To convert to odds for, use p/(1-p). To convert to odds against, use (1-p)/p. For example, if p = 0.25: percentage = 25%, odds for = 0.25/0.75 = 1:3, odds against = 0.75/0.25 = 3:1. To convert odds (a:b) to probability, use a/(a+b).