What does E^c represent in probability?

In probability, E^c signifies the complement of the event E. This means that E^c includes all the outcomes in the sample space that are not part of event E. When considering an event E, the complement E^c represents every possible scenario where E does not occur.

For example, if E is the event of rolling a 3 on a six-sided die, then E^c would encompass all the outcomes where a 3 is not rolled (1, 2, 4, 5, or 6). Therefore, E^c effectively captures the occurrence of everything outside of event E. Understanding this concept is crucial in probability, as it allows you to easily calculate the likelihood of events not happening, which can often be useful in problem-solving scenarios.