Events:

The basis of probability is the idea of an event. An event is just something which may or may not happen, like a tossed coin landing heads or snow falling on the roof of the Meteorological Office in London on 25 December this year. In some cases it is useful to think of an event as the outcome of a trial. for example, the trial of tossing a coin is usually reckoned to have two possible outcomes (heads and tails). As a technical term we call the set of possible outcomes to a trial the sample space (in this case the set $\{ heads, tails\}$).

Treating the outcomes of the coin toss as the sample space is a question of point-of-view. It's perfectly possible to imagine a sequence of trials each consisting of watching someone rolling a (hidden) dice to decide whether or not to toss a coin or draw a coloured ball from an urn. The result of the coin-toss or the draw is visible. In this case the sample space of a whole trial is $\{red,black,heads,tails\}$ and the coin-toss itself would be an event. We often want to pick out the primitive events, namely $\{heads\}$,$\{tails\}$,$\{red\}$ and $\{black\}$, and distinguish them from compound events which can be decomposed into disjunctions of primitive events like $\{ heads, tails\}$ (which means ``heads'' or ``tails'').

Now imagine repeatedly tossing a coin, keeping track of heads and tails. It is reasonable to suppose that the successive trials are unaffected by the outcome of previous trials. It is also reasonable to expect that over time an unbiased coin will give approximately equal numbers of heads and tails, and that the ratio between heads and tails will more closely approximate to unity as the number of trials increases. This is actually quite a deep result, but we won't go into it further. It's also true that for a biased coin the ratio between heads and tails will eventually settle down to some value (could be 0.57) if you have enough trials.