Calculate probabilities for single events, two events, at least one occurrence, and conditional probability.
Quick Answer:Enter event probabilities (as decimal 0-1 or percentage) and select a mode to calculate complement, intersection, union, and odds ratio instantly.
Main Result
Calculating...
Complement P(not A)
--
Intersection P(A and B)
--
Union P(A or B)
--
Odds Ratio (A)
--
A common probability mistake is the "gambler's fallacy" -- believing that past outcomes affect future independent events. Each coin flip is always 50/50 regardless of previous results. When combining probabilities, always verify whether events are truly independent before using P(A and B) = P(A)*P(B). In real-world scenarios, most events have some degree of dependence.
Independent events are those where the outcome of one event does not affect the outcome of the other. For example, flipping a coin and rolling a die. For independent events, P(A and B) = P(A) * P(B). Dependent events are those where the outcome of one event affects the probability of the other, like drawing cards without replacement.
The probability of at least one event occurring in n independent trials is P(at least one) = 1 - (1 - P(A))^n. This uses the complement rule: instead of calculating every possible success scenario, you calculate the probability of zero successes and subtract from 1. For example, rolling at least one 6 in 4 rolls is 1 - (5/6)^4, about 51.8%.
Conditional probability P(A|B) is the probability of event A occurring given that event B has occurred. It is calculated as P(A|B) = P(A and B) / P(B). Bayes' theorem extends this: P(A|B) = P(B|A) * P(A) / P(B). This is fundamental in statistics, machine learning, and medical testing for updating probability estimates with new evidence.