Conditional probability is when the probabililty of an event is dependent on the outcome of another event.

The probability that event \(B\) occurs given that event \(A\) has occurred is written is \(P(B|A)\).

\(P(B|A) = \dfrac{P(B∩A)}{P(A)}\)

Alternatively:

\(P(B|A)×P(A) = P(B∩A) \)

For independent events:

\(P(B|A) = P(B|A') = P(B) \)