Sample Space
Set of all possible outcomes for an experiment
In probability theory, the sample space is the set of all possible outcomes of a random experiment. It is denoted by the symbol S and can be defined in many different ways, depending on the specific problem.
For example, if we flip a coin once, the sample space is {heads, tails}. If we roll a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. If we draw two cards from a deck of 52 cards, without replacement, the sample space is the set of all possible pairs of cards that can be drawn, which is given by (52 choose 2) = 1326.
The sample space is a fundamental concept in probability theory, as it defines the basic set of outcomes that we are interested in analyzing. The events in a probability problem are subsets of the sample space, and the probability of an event is the number of outcomes in that event divided by the total number of outcomes in the sample space.
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