What is a conditional probability in a two-way table?
Conditional probability is the probability of an event given the probability of another event. With reference to a two way table it is most often the probability of an event identified by a column (or row) given an event identified by a row (or column).
This is most easily seen with an example:
Suppose students are taking Math classes from one of 3 teachers; students have recently taken a standardized test and received alphabetic grades. Counts of the number of students who received each possible grade within each class have been collected as displayed in the two-way table below.
One possible question that might be asked is
"What is the probability that a student randomly selected from Mrs. X's class got an F?"
Typical notation for conditional probability is of the form:
For our example we are asked for
Although there are 107 students recorded in our table, only 38 of them are in Mrs. X's class and
Of course, the problem may be more complex and we might be asked for
but the methodology of solution remains simple.