Compatible and Incompatible Events
Events are classified as compatible or incompatible, depending on whether they can occur simultaneously.
- Compatible Events
Two events are compatible if both can take place at the same time. - Incompatible Events
Two events are incompatible if the occurrence of one event prevents the other from occurring at the same time.
A Practical Example
A classic example of incompatible events is flipping a coin:
Consider the following two events:
- E1: The coin lands on "heads" after being flipped.
- E2: The coin lands on "tails" after being flipped.
If the coin lands on "heads" in a single flip, it cannot also land on "tails" in that same flip, and vice versa.
Thus, E1 and E2 are incompatible events because they cannot occur simultaneously in a single coin flip.
Example 2
A bag contains 10 pieces of fruit: 4 apples, 3 pears, and 3 oranges.
Consider the following events:
- E1: Drawing an apple from the bag.
- E2: Drawing a fruit that is not an orange.
If I draw an apple from the bag, both events E1 (since I drew an apple) and E2 (since an apple is not an orange) happen simultaneously.
Therefore, events E1 and E2 are compatible because they can occur at the same time.
And so forth.
