Define sample space in probability.

The sample space in probability is the set of all possible outcomes of an experiment.

In probability theory, an experiment is any process that generates a set of possible outcomes. The sample space is the set of all possible outcomes of that experiment. For example, if we toss a coin, the sample space is {heads, tails}. If we roll a dice, the sample space is {1, 2, 3, 4, 5, 6}. If we draw a card from a deck of 52 cards, the sample space is {Ace of hearts, 2 of hearts, 3 of hearts, ..., King of spades}.

The sample space is denoted by the symbol S. It is important to note that the sample space must be exhaustive and mutually exclusive. Exhaustive means that every possible outcome of the experiment must be included in the sample space. Mutually exclusive means that no two outcomes in the sample space can occur at the same time.

The sample space can be finite or infinite. If the sample space is finite, we can count the number of possible outcomes by using the formula:

n(S) = number of elements in the sample space

For example, if we toss a coin, n(S) = 2. If we roll a dice, n(S) = 6.

If the sample space is infinite, we cannot count the number of possible outcomes. In this case, we use other methods to describe the sample space, such as intervals or functions.