Question

in parts (a) and (b), identify whether the events are disjoint, 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
disjoint
neither
b) you and your class partner both earn as in this course.
disjoint
independent
neither
c) if two events can occur at the same time, they must be independent.
true
false

Explanation:

a)

Two events are disjoint if they cannot occur at the same time. Here, you and a randomly - selected student can both earn A's, so they are not disjoint. Independent events mean the occurrence of one does not affect the occurrence of the other. While there could be some minor correlations in a class (e.g., overall class difficulty), generally, your grade and a randomly - selected student's grade are not directly influencing each other, so they are independent.

b)

You and your class partner's grades may be related. For example, you may study together, share resources, etc. So the occurrence of one getting an A may affect the other getting an A. They are not disjoint as both can get A's, and they are not independent due to the relationship, so they are neither.

c)

Just because two events can occur at the same time does not mean they are independent. Independence is about the non - influence of one event on the other's probability of occurring. For example, in a class, two friends' grades can occur simultaneously but may be related due to studying together, so this statement is false.

Answer:

a) independent
b) neither
c) false