Question

define mutually exclusive events in your own words. choose the correct answer below. a. two events that have the same probability are called mutually exclusive events. b. two events that can both occur at the same time are called mutually exclusive events. c. two events that cannot both occur at the same time are called mutually exclusive events. d. two events that have only one possible outcome are called mutually exclusive events.

Explanation:

To determine the correct definition of mutually exclusive events, we analyze each option:

• Option A: Having the same probability is not the definition of mutually exclusive. For example, rolling a 1 and rolling a 2 on a die have the same probability but are mutually exclusive, but this is not the defining characteristic. So A is incorrect.
• Option B: If two events can both occur at the same time, they are not mutually exclusive (they are called non - mutually exclusive or overlapping events). So B is incorrect.
• Option C: By definition, mutually exclusive events are events where the occurrence of one event precludes the occurrence of the other event, meaning they cannot both occur at the same time. This matches the definition.
• Option D: Having only one possible outcome is the definition of a simple event, not mutually exclusive events. For example, rolling a 1 on a die is a simple event, and rolling a 2 is another simple event, and they are mutually exclusive, but the definition of mutually exclusive is not about the number of outcomes of the events themselves. So D is incorrect.

Answer:

C. Two events that cannot both occur at the same time are called mutually exclusive events.