Conditional probability
A conditional probability is one that is computed under the assumption that some related event is known to have occurred. For example, in the marble experiment, if we know that the first marble drawn was red, then the probability that the second marble is green is 4/5 = 80%. This is a conditional probability, the condition being that the first marble was red. It is written as:
(The vertical bar symbol | is read as "given").
On the other hand, the (unconditional) probability that the second marble is green is:
It should seem sensible that the probability that the second marble is green is greater (80%) after having removed a red marble. It should also seem sensible that the unconditional probability of green on the second (67%) is the same as the probability that the first is green (4/6).
The general formula for the conditional probability of an event F, given an event E, is
The symbolism E ∩ F means "E and F".
To apply this formula to our marbles example, let E be the...
