Probability Calculator

Enter the probabilities of Event A and Event B (values between 0 and 1) to calculate P(A and B), P(A or B), P(A|B), and other key compound probability results. Switch to Series Mode to find the probability of an event occurring across multiple independent trials. You get a full breakdown of union, intersection, conditional, and complement probabilities.

Enter a value between 0 and 1

Enter a value between 0 and 1

Probability of the event occurring in a single trial

How many independent trials are performed

Results

P(A ∩ B) — Both Events Occur

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P(A ∪ B) — A or B Occurs

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P(A XOR B) — Exactly One Occurs

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P(A') — A Does NOT Occur

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P(B') — B Does NOT Occur

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P(Neither A nor B)

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P(A | B) — A Given B

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P(B | A) — B Given A

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P(At Least One Occurrence in Series)

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P(No Occurrences in Series)

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P(Exactly One Occurrence in Series)

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Probability Breakdown

Frequently Asked Questions

What is probability and how is it measured?

Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means it is certain. For example, a fair coin flip has a probability of 0.5 for heads.

What is the difference between P(A and B) and P(A or B)?

P(A and B), also written P(A ∩ B), is the probability that BOTH events occur simultaneously. For independent events, this equals P(A) × P(B). P(A or B), written P(A ∪ B), is the probability that AT LEAST ONE of the events occurs, calculated as P(A) + P(B) − P(A ∩ B).

What does XOR probability mean?

XOR (exclusive OR) probability is the chance that exactly one of the two events occurs, but not both. It equals P(A) + P(B) − 2 × P(A ∩ B). This is useful when you want to know the likelihood of one outcome or the other, but not both at the same time.

What is conditional probability P(A | B)?

Conditional probability P(A | B) is the probability that event A occurs given that event B has already occurred. For independent events, P(A | B) equals P(A), because B's occurrence does not affect A. It is calculated as P(A ∩ B) / P(B).

How does the series probability calculator work?

The series calculator finds probabilities across multiple independent trials of the same event. It uses the binomial formula: P(at least one) = 1 − (1 − p)^n, where p is the single-trial probability and n is the number of trials. This is useful for things like rolling a die multiple times or repeated independent tests.

What does 'independent events' mean in probability?

Two events are independent if the occurrence of one does not affect the probability of the other. For example, flipping a coin and rolling a die are independent events. This calculator assumes all events are independent when computing compound probabilities.

What is the complement of a probability?

The complement of an event A is the probability that A does NOT occur, denoted P(A') or P(not A). It is simply 1 − P(A). For example, if the probability of rain is 0.3, then the probability of no rain is 0.7.

Can I enter probabilities greater than 1?

No. Probabilities must be between 0 and 1 inclusive, where 0 represents impossibility and 1 represents certainty. If you have a percentage (e.g. 60%), divide by 100 to convert it to a decimal (0.60) before entering it into the calculator.

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