In probability theory, the sample space refers to the set of all possible outcomes of a random experiment. It is denoted by the symbol “S”.
For example, consider a fair six-sided die. The sample space for this experiment would be S = {1, 2, 3, 4, 5, 6}, since these are the possible outcomes when rolling the die.
An event, on the other hand, is a subset of the sample space. It represents a particular outcome or a combination of outcomes that we are interested in. It is denoted by a capital letter such as “A,” “B,” or “E”.
The number of events in probability theory can vary depending on the experiment and the specific outcomes of interest. In general, an event can consist of a single outcome or multiple outcomes from the sample space.
For example, if we define event A as rolling an even number on the six-sided die, then A = {2, 4, 6}. This event consists of three outcomes from the sample space. Alternatively, event B could be defined as rolling a number greater than 4, and B = {5, 6}, which consists of two outcomes.
The number of events can be finite or infinite, depending on the nature of the experiment. In some cases, the entire sample space can be considered as an event, which is referred to as the certain event and is denoted by “S”.