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.
independent
neither
mutually exclusive
b) you and your class partner both earn as in this course.
mutually exclusive
neither
independent
c) if two events can occur at the same time, they must be independent.
false
true

Explanation:

Step1: Define mutually - exclusive and independent events

Mutually exclusive events cannot occur at the same time. Independent events: the occurrence of one does not affect the occurrence of the other.

Step2: Analyze part (a)

Your grade and a randomly - selected student's grade may not affect each other. So the events are independent.

Step3: Analyze part (b)

You and your class partner may study together, help each other, etc. The occurrence of one getting an A may affect the other getting an A. Also, both can get A's, so they are not mutually exclusive. So they are neither mutually exclusive nor independent.

Step4: Analyze part (c)

Just because two events can occur at the same time does not mean they are independent. For example, in a deck of cards, drawing a red card and drawing a heart are not independent (since a heart is red), but they can occur at the same time. So the statement is false.

Answer:

a) Independent
b) Neither
c) False