# Conditional Probability

The contingency table exercise is a hard concept to grasp for most people. I have heard things like ‘I don’t know when to use the numbers directly from the table’. I have also seen students do excessive calculations when the table the answer was in the table. I want to speak on the scenario where you are given a continguency table full of the frequencies and not wholeenumbers. When you use the table, think about the conditional probability equation. The equation has the intersect of two events over the probability of a particular event. I am speaking of the multiplication rule for conditional probability.

P(A∩B)=P(A)P(B|A)

or

P(A∩B)/P(A)=P(B|A)

The intersect of the two events in question will always be in the table. If it’s in the table you won’t have to calculate it using the multiplication rule. The only time you use an equation is when you are (1) not given the contingency table or (2) you are being asked to calculate the probability of an event given another event. Otherwise, use the table. The contingency table with frequency counts will only give you intersections  [ etc. P(A∩B) ] or specific probabilities [etc. P(A)].

It feels like torture but there is some logic to it.