AND Probability Calculator

Enter the probability of Event A and Event B (values between 0 and 1) to calculate their joint probability P(A∩B) — the chance both events occur together. Choose whether the events are independent or dependent, and get the intersection probability plus supporting results like P(A∪B), P(A only), P(B only), and P(neither) all at once.

Event Relationship *

Independent: P(A∩B) = P(A) × P(B). Dependent: provide P(B|A) instead.

Enter a value between 0 and 1.

Enter a value between 0 and 1.

Only used when events are dependent.

Results

P(A AND B) — Joint Probability

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P(A OR B) — Union

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P(A only) — A but not B

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P(B only) — B but not A

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P(Neither A nor B)

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Joint Probability as Percentage

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Frequently Asked Questions

How do I find the probability of A and B?

For independent events, multiply the individual probabilities: P(A∩B) = P(A) × P(B). For dependent events, use the conditional formula: P(A∩B) = P(A) × P(B|A), where P(B|A) is the probability of B occurring given that A has already occurred.

What is the formula for the joint probability of independent events?

The joint probability formula for independent events is P(A∩B) = P(A) × P(B). This works because when two events are independent, the occurrence of one does not affect the probability of the other.

What is the probability of obtaining two heads in two coin tosses?

Each coin toss has a probability of 0.5 for heads. Since the tosses are independent, P(heads AND heads) = 0.5 × 0.5 = 0.25, or a 25% chance of getting two heads in a row.

What does P(A∩B) represent?

P(A∩B) represents the probability that both event A and event B occur simultaneously. It is also called the joint probability or the intersection of A and B. The ∩ symbol denotes 'AND' or intersection in set theory.

What is the difference between independent and dependent events?

Independent events are those where the outcome of one event does not affect the other — for example, flipping two coins. Dependent events are those where the outcome of one event influences the probability of the other — for example, drawing cards from a deck without replacement.

How do I calculate P(A∩B) for dependent events?

For dependent events, the formula is P(A∩B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given A. You must know or be able to estimate this conditional probability — it accounts for how A's occurrence changes the likelihood of B.

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

P(A∩B) is the probability that BOTH A and B occur (AND). P(A∪B) is the probability that AT LEAST ONE of them occurs (OR). The relationship between them is: P(A∪B) = P(A) + P(B) − P(A∩B).

Can the joint probability ever be greater than either individual probability?

No. The joint probability P(A∩B) can never exceed either P(A) or P(B) individually, because the intersection is a subset of each individual event. It will always be less than or equal to the smaller of the two individual probabilities.