An Event is a subset of a sample space.
Remember, a sample space is a set of all possible outcomes. For example, the sample space for a mode choice in a given area could be:
\[ S = {\{Car, \ Bus, \ Bicycle}\} \]
Then, an event A might be:
\[ A = {\{ Car }\} \]
A is an event because it is a subset of S.
Probability is a number assigned to each event in the sample space such that:
1. Probability of any event is non-negative
2. Probability of sample space is 1
3. If the events are disjoint, i.e. \[ A \cap B = \varnothing \] for any 2 events A and B, then the probability of a finite union (or countably infinite union) of the events is the sum of probabilities of individual events, i.e. \[ P(A \cup B) = P(A) + P(B) \]
The number which is assigned to an event is usually the relative frequeny. Relative frequency is calculated by the dividing the number of outcomes of an event to the total number of outcomes.