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Probability Calculator

Free probability calculator: instantly find P(A and B), P(A or B) and conditional probabilities for independent or dependent events with clear results.

Probability questions show up everywhere: the chance it rains and traffic is heavy, the odds of drawing an ace, or the chance at least one of two independent events happens. The common mistakes are double-counting overlaps and confusing independent with conditional events.

This probability calculator handles two events, A and B, and returns P(A and B), P(A or B) and both conditional probabilities. Switch between independent and dependent events — for dependent events, enter P(B|A), the probability of B given that A has already happened.

Students use it for statistics homework, while anyone making everyday forecasts can check their intuition against the numbers.

Enter both probabilities as percentages (0-100) and choose the relationship between the events; all results update instantly.

50%
0100
50%
0100
Example
Example: Rain and Traffic

Suppose P(A) = 30% (it rains), P(B) = 50% (traffic is heavy), and P(B|A) = 60% (when it rains, traffic is heavy 60% of the time). In dependent mode:

P(A and B) = 30% × 60% = 18%
P(A or B) = 30% + 50% − 18% = 62%
P(A|B) = 18% / 50% = 36%

There is an 18% chance of both, and a 62% chance that at least one happens.

Key Insight: If the events were independent, P(A and B) would be 30% × 50% = 15% — dependence changes the joint probability, so always set the mode correctly.

Frequently Asked Questions

How do I find the probability of A or B?

Add the two probabilities, then subtract the overlap: P(A or B) = P(A) + P(B) − P(A and B). Without subtracting, the overlap is counted twice.

What does "independent" mean?

Events are independent when one does not change the probability of the other: P(A|B) = P(A), so P(A and B) = P(A) × P(B). Two coin flips are a classic example.

What is conditional probability?

P(A|B) = P(A and B) / P(B): the probability that A happens given that B has already happened. It only makes sense when P(B) > 0.

How do I calculate probability for three events?

For independent events, multiply: P(A and B and C) = P(A) × P(B) × P(C). For the union of three events use inclusion-exclusion: P(A∪B∪C) = P(A)+P(B)+P(C) − P(A∩B) − P(A∩C) − P(B∩C) + P(A∩B∩C).

Probabilities must be between 0% and 100%. This calculator covers two events; for three or more independent events, multiply the probabilities. Normal-distribution probability (e.g. "probability calculator normal distribution") is a different task — use the z-score calculator instead.

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