Search results
Results from the WOW.Com Content Network
An event, however, is any subset of the sample space, including any singleton set (an elementary event), the empty set (an impossible event, with probability zero) and the sample space itself (a certain event, with probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential ...
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.
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. [note 1] [1] [2] A simple example is the tossing of a fair (unbiased) coin. Since the ...
In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events , hence the name.
(The conversion to log form is expensive, but is only incurred once.) Multiplication arises from calculating the probability that multiple independent events occur: the probability that all independent events of interest occur is the product of all these events' probabilities. Accuracy.
Given two events A and B from the sigma-field of a probability space, with the unconditional probability of B being greater than zero (i.e., P(B) > 0), the conditional probability of A given B (()) is the probability of A occurring if B has or is assumed to have happened. [5]
Another example of events being collectively exhaustive and mutually exclusive at same time are, event "even" (2,4 or 6) and event "odd" (1,3 or 5) in a random experiment of rolling a six-sided die. These both events are mutually exclusive because even and odd outcome can never occur at same time.