Inferential Statistics : Probability and distributions 2

Hi there!

Today we'll discuss marginal probability.

Marginal probability is all about computing the probability of an event occurring given that it is a part of a subset of another event.

P.S. If the above definition does not make sense, hang in there. You'll get it by the end of the post.

We use contingency tables to compute marginal probability.

Contingency table consists of rows and columns of two attributes at different levels with frequencies or numbers in each of the cells. It is a matrix of frequencies assigned to rows and columns.

The term marginal is used to indicate that the probabilities are calculated using a contingency table.

Example : Of cars on a used car lot, 70% have air conditioning (AC) and 40% have a CD player. 20% of cars have both. What is probability that a car has a CD player given that it has AC?

Assumption : There are 100 cars in total.

Here is the contingency table :

The data that we have derived from the problem statement has been highlighted in yellow. The rest of the values were derived from simple arithmetic.

The probability that a car has a CD player given that it has an AC is clearly 30/70 = 3/7.

This was marginal probability in a nutshell.

Thank you!