Sample Space vs Event

The sample space lists every outcome that could occur, and the probabilities across it sum to 1. For example, the sample space for flipping two coins is $\{HH, HT, TH, TT\}$, four equally likely outcomes. An event is any subset of the sample space, such as getting exactly one head. Writing out the sample space is often the first step in computing a probability.

An event is any set of outcomes you might care about, and its probability is the chance that the outcome lands inside it. For example, when rolling a die, the event of rolling an even number is the subset $\{2, 4, 6\}$. For equally likely outcomes, $P(\text{event}) = \frac{\text{outcomes in the event}}{\text{total outcomes}}$, so this event has probability $3/6 = 0.5$. Events can be combined with and, or, and not to build new events.