Question

HYPER, a company that helps clients build technology-based businesses, released the results of a 2019 study of how full-time workers keep and manage their passwords at work. Some results: 35% of workers keep their passwords in a notebook, in an Excel file, or on a sticky note: 57% had to reset a password they forgot; and 19% have over ten passwords to manage. A full-time worker is randomly selected.

a. Are the two events, A = {the worker has over ten passwords to manage and B = {the worker had to reset a password he/she forgot}, mutually exclusive? Explain.

Answer 1

The events A and B are not mutually exclusive because it is possible for a worker to have over ten passwords to manage and also have to reset a password they forgot.

Step-by-step explanation:

The two events, A = {the worker has over ten passwords to manage} and B = {the worker had to reset a password he/she forgot}, cannot be mutually exclusive.

Mutually exclusive events are events that cannot occur at the same time. In this case, it is possible for a worker to have over ten passwords to manage and also have to reset a password they forgot. For example, a worker who has fifteen passwords to manage may still forget one of them and have to reset it.

Therefore, events A and B are not mutually exclusive.