Conditional probability calculator

Formula

How it works

P(A|B) is the probability of A once we know B has happened: the chance of both happening, divided by the chance of B alone. Events are independent when knowing one happened does not change the probability of the other, which is when P(A ∩ B) equals P(A) × P(B).

Worked example

The same calculation with the default values:

• P(A) 40 %
• P(B) 50 %
• P(A and B) 25 %

1. P(A|B) = 0.25 ÷ 0.5 = 50%
2. P(B|A) = 0.25 ÷ 0.4 = 62.5%

Result: P(A | B): 50% · P(B | A): 62.5% · Independence: A and B are dependent

Common mistakes

• Confusing P(A|B) with P(B|A) - these answer different questions and are generally different numbers; mixing them up is one of the most common errors in probability (and in real-world reasoning about test results, for instance).
• Using P(A) instead of P(A ∩ B) in the numerator - conditional probability specifically needs the probability of both events happening together, not just event A on its own.
• Forgetting that P(B) in the denominator must be non-zero - conditioning on an event that cannot happen is undefined, not just a very small probability.