Problem 100d

Given information

A college finds that  of students have taken a distance learning class and that  of students are part time

students. Of the part-time students,  have taken a distance learning class. Let  event that a student takes a distance

learning class and  event that a student is a part time student.

Step-by-step explanation

The two events are independent if the below three conditions are satisfied:

,

,

Here, Event that a student takes a distance learning class,

Event that a student is a part time student.

,

,

,

.

It is clear that,

The first condition is not satisfied.

Therefore, the events are not independent.

Hence, the events  and  are not independent.