Search results
Results from the WOW.Com Content Network
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (with respect to the probability measure). [1] In other words, the set of outcomes on which the event does not occur has probability 0, even though the set might not be empty.
In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
The probabilities of rolling several numbers using two dice. Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.
In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events. [4] Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as
That is, for an event A, = (). Equivalently, the probabilities of an event and its complement must always total to 1. This does not, however, mean that any two events whose probabilities total to 1 are each other's complements; complementary events must also fulfill the condition of mutual exclusivity.
Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. [note 1] For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often ...