When we compute the probability of event F assuming that the event E has already occurred, we call this the conditional probability of F given E.
We denote this probability as P(F|E). We read P(F|E) as “the probability of F given that E has occurred”, or in a quicker way, “the probability of F given E.”
If E and F are dependent events in a sample space with equally likely outcomes, then:
If E and F are dependent events in a sample space, then
This formula can also be rearranged algebraically for P(E⋂F) by multiplying both sides by P(E).
Events E and F are independent events if P(E|F) = P(F). In other words, if P(E|F) ≠ P(F), then E and F are dependent.