Joint Probability Tables
You are wondering whether the moon has an influence upon a wolf pack howling.
You categorize the nights the pack is outside by being a full moon, new moon, or another kind of moon.
You categorize the nights on whether the pack howls or not.
You create the following table (called a two way joint probability table) and write the relative frequencies.
What does x equal?
What is the probability that it will be full moon and the wolves do not howl?
Marginal Probabilities
Marginal probabilities get their name from being written down the sides of the table. These can be found by adding up the joint probabilities in each row or column.
Before we categorized events in two different ways marginal probabilities were just the probabilities of an event occurring.
See below.
Marginals Must be Mutually Exclusive
Within each categorization the events should not be overlapping. So it would be incorrect to categorize the wolves as howling, not howling, or migrating since wolves could hunt and do either of those things. This could also lead the total probability being greater than 1.
Beyond the categorization there is also one other pair of events that are mutually exclusive. Which are they?