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A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
In probability theory, particularly information theory, the conditional mutual information [1] [2] is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
Information diagrams have also been applied to specific problems such as for displaying the information theoretic similarity between sets of ontological terms. [ 3 ] Venn diagram showing additive and subtractive relationships among various information measures associated with correlated variables X and Y .
Venn diagram of information theoretic measures for three variables x, y, and z, represented by the lower left, lower right, and upper circles, respectively. The interaction information is represented by gray region, and it is the only one that can be negative.
Each node on the diagram represents an event and is associated with the probability of that event. The root node represents the certain event and therefore has probability 1. Each set of sibling nodes represents an exclusive and exhaustive partition of the parent event. The probability associated with a node is the chance of that event ...
The probability of the event that the sum + is five is , since four of the thirty-six equally likely pairs of outcomes sum to five. If the sample space was all of the possible sums obtained from rolling two six-sided dice, the above formula can still be applied because the dice rolls are fair, but the number of outcomes in a given event will vary.
Buffon's needle was the earliest problem in geometric probability to be solved; [2] it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is =.