Two events are __?__ events if they are disjoint events and one event or the other must occur.
One or the other must occur means that the two events make up the sample space, like heads and tails in tossing of a coin.
These events are then called complementary. In a Venn diagram, the universal set (&Omega) or sample space is divided into two parts, so that any outcome must fall into one or the other event.
Two events are mutually exclusive events if they are disjoint events and one event or the other must occur.
To determine if two events are mutually exclusive, you can follow these steps:
1. Identify the two events: Let's call them Event A and Event B.
2. Check if the events are disjoint: If Event A and Event B have no outcomes in common, meaning that they cannot both occur simultaneously, then they are disjoint events.
3. Determine if one event or the other must occur: If Event A or Event B (or both) must occur, then they are mutually exclusive. This means that the occurrence of one event excludes the possibility of the other event happening.
For example, let's consider the events of flipping a coin: Event A is getting a heads, and Event B is getting a tails. Since it is not possible to get both heads and tails at the same time, these events are disjoint. Also, since flipping a coin guarantees either heads or tails, Event A or Event B must occur. Therefore, Event A and Event B are mutually exclusive events.