Probability Calculator
Find P(A), P(A∩B), P(A∪B) & More
Calculate single event probability, combined "AND" / "OR" probability, and complement instantly — with full step-by-step working. Built for TN Board, CBSE, JEE and NEET students.
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How to Calculate Probability
The probability of a single event is calculated as the number of favorable outcomes divided by the number of total possible outcomes. Probability always lies between 0 (impossible) and 1 (certain).
P(A) = Favorable Outcomes / Total Outcomes
For two events, there are two common combinations tested in exams. P(A and B) — both events happening — is found by multiplying P(A) × P(B) if the events are independent (one doesn't affect the other), or by using the given P(A∩B) if they are dependent. P(A or B) — at least one event happening — uses the addition rule: P(A) + P(B) − P(A∩B), which avoids double-counting outcomes where both events occur together.
The complement of an event, written P(A'), is the probability that A does not happen, calculated simply as 1 − P(A). This is useful for "at least one" problems, where it's often easier to calculate the probability that something doesn't happen at all, then subtract from 1.
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Independent events don't affect each other — like flipping a coin and rolling a die, where the outcome of one has no bearing on the other. Dependent events do affect each other — like drawing two cards from a deck without replacement, where the first draw changes the probabilities for the second. Independent events use P(A) × P(B) for "and"; dependent events need the actual P(A∩B) value or conditional probability.
When you add P(A) and P(B) directly, any outcome where both A and B happen gets counted twice — once in each probability. Subtracting P(A∩B) removes that double-count, so P(A) + P(B) − P(A∩B) gives the correct probability that at least one of the events occurs.
No — probability always lies between 0 and 1 inclusive, where 0 means the event is impossible and 1 means it's certain. If a calculation gives a value outside this range, it usually means the inputs given (like P(A∩B) being larger than either individual probability) are inconsistent or entered incorrectly.
The complement rule (P(A') = 1 − P(A)) is especially useful for "at least one" problems, which are common in board exams and competitive tests. Instead of calculating every way an event could happen at least once, it's often far simpler to calculate the probability it never happens, then subtract from 1.
Yes — probability is a core topic in Class 11-12 Maths, and these same "and"/"or"/complement rules appear regularly in JEE, NEET (through Biology and Physics applications), and TNPSC quantitative aptitude sections. Check the step-by-step section after calculating to understand the method, not just the final answer.