(
Probability:)
A
measurable set of
points in the
measure space of the
probability measure.
What this means, in plain English (as opposed to math gibberish) is a set of possible outcomes to which we can assign a probability. For various unpleasant technical reasons we cannot assign probabilities to all sets of outcomes. But we can assign a probability to any set of outcomes which can be described "naturally".
Since events are sets, they're traditionally written inside squiggly brackets.
Examples:
- If our probability space is the roll of a fair 6-sided die, then {1 is rolled} and {an even number is rolled} are both events.
- If our probability space is an infinite series of coin tosses, these are all events (note that each event is a subset of the preceding event):
- {Infinitely many tosses come up heads}.
- {There exists an N for which the proportion of heads out of the first n tosses is between 0.4 and 0.6 for all n>=N}.
- {The proportion of heads out of the first n tosses tends to 0.5 as n tends to infinity}.
If our probability space is tomorrow's weather, then {it will rain tomorrow} is an event, but {it will be sunny the day after tomorrow} is not an event (knowing tomorrow's weather does not determine the following day's weather exactly!).