Question

Determine whether the two events are disjoint for a single trial.​ (Hint: Consider​ "disjoint" to be equivalent to​ "separate" or​ "not overlapping".) Randomly selecting a car from the vehicle assembly line and getting one that is free of defects. Randomly selecting a car from the vehicle assembly line and getting one with a dead battery. Choose the correct answer below. A. The events are disjoint. The first event is the complement of the second. B. The events are disjoint. They cannot occur at the same time. C. The events are not disjoint. They can occur at the same time. D. The events are not disjoint. The first event is not the complement of the second.

Answer 1

Answer: Hello there!  

we have two events and we want to see if they are disjoint, where disjoint means that they are "not overlapping" or that "cant occur at the same time"):

Randomly selecting a car from the vehicle assembly line and getting one that is free of defects.

Randomly selecting a car from the vehicle assembly line and getting one with a dead battery.

Clearly, if the car you got has a dead battery, it has a defect, then bot events cant occur at the same time.

now let's analyze the options:

A. The events are disjoint. The first event is the complement of the second.  

There are other defects that can occur to the car, then the options aren't complementary, because they don't cover all the options.

B. The events are disjoint. They cannot occur at the same time.

As I said before, this is true!

C. The events are not disjoint. They can occur at the same time

This is false, as i said before the dead batery implies a defect in the car, then both events can not happend at the same time.

D. The events are not disjoint. The first event is not the complement of the second.

It is true that the first event is not the complement of the second, but the events are disjoint, so this is false.

then the correct option is option C.