Definition
Conditional probability
The probability of an event after a known condition narrows the possible outcomes.
What it means
First use the word given to shrink the possible outcomes to those where the condition is true. Then find the chance of the event inside that smaller set.
Remember it
Given means shrink the list first.
Example
One card is drawn at random from cards numbered 1 to 6. Given that the number is even, the possible results are 2, 4, and 6. Two of those are greater than 3, so the conditional probability is 2/3.
Watch for
P(A|B) is defined only when P(B) is greater than 0, and it need not equal the original probability P(A).
Common mix-up
P(A|B) asks for A given B; reversing the order to P(B|A) asks a different question.
Exact meaning
The conditional probability of event A given event B is P(A|B) = P(A ∩ B) / P(B), provided P(B) > 0.