Question

A recent survey asked UF students if they had a job or not, and if they were underclassmen (Freshmen and Sophomores) or upperclassmen (Juniors and Seniors). The answers appear on the table below.
JOB NoJob
Underclassmen 40 37 77
Upperclassmen 42 39 81
82 76 158

Let A be the event that a student has a job, and let B be the event that a student is an underclassmen. Find P(AUB).

Answer 1

Following the table and knowing that the total number of students interviewed were 158 ( we can see this by looking adding either the total number of upperclassment or adding the total number of people with jobs or no jobs, this value is at the bottom right of the table in the figure attached).
Recall that:
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
In the figure provided each of these terms is highlighted in a different color. To convert these values to their matching probabilities we have to divide each by the total number of students, this is due to the fact that the probability is the number of favorable cases (in this case a group matching the qualities we seek) divided by the total amount of cases ( that is the total number of people interviewed). In the figure the answer is provided. For the intersection of the two events we're looking for people that is both an undercalssman and also has a job.