Question

in parts (a) and (b), identify whether the events are mutually exclusive, independent, or neither (events cannot be both disjoint and independent).
a) you and a randomly selected student from your class both earn as in this course.
mutually exclusive
independent
neither
b) you and your class partner both earn as in this course.
mutually exclusive
independent
neither
c) if two events can occur at the same time, they must be independent.
false
true

Explanation:

a)

Two students earning A's are not mutually - exclusive as both can happen simultaneously. Also, the performance of one student may not affect the other's performance in a random selection, so they are independent.

b)

You and your class partner's grades may be related as you may study together and influence each other's performance, so they are not independent. And both can earn A's, so not mutually exclusive. Thus, neither.

c)

Just because two events can occur at the same time does not mean they are independent. Dependence can exist even when events are not mutually exclusive. So false.

Answer:

a) Independent
b) Neither
c) False