To explain what marginal probability is, we need a contingency table. A contingency table is a table in which we show the frequency for 2 variables.

One variable is used to categorize rows and the other is used to categorize columns.

For example, suppose a company specializes in training students to pass the GED test. The company had 200 students last year.

The following contingency table shows their success rates broken down by gender.

In the table above, the variable that categorizes rows is gender. This variable can be male or female.

The variable that categorizes columns is the result. This variable can pass or fail.

Did you notice any of the following?

• The number of men + women = 102 + 98 = 200
• Number of passed students + failed students = 114 + 86 = 200
• The number of women who failed the GED test is 30

Now that you know what a contingency table is, what is the marginal probability?

There are 4 events in the table above.

The probability of each of these 4 events is called marginal probability or simple probability

The 4 marginal probabilities can be calculated as follows

P (a student is a man) =

Number of men
/
Total number of students

P (a student is a man) =

102
/
200

= 0.51

P (a student is a woman) =

Number of females
/
Total number of students

P (a student is a woman) =

98
/
200

= 0.49

P (a student passed) =

Number of passed students
/
Total number of students

P (a student passed) =

114
/
200

= 0.57

P (one student failed) =

Number of students who failed
/
Total number of students

P (one student failed) =

86
/
200

= 0.43

The marginal probabilities are given on the right and at the bottom of the table below.