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In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. [1] The event A and its complement [not A] are mutually exclusive and exhaustive. Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A.
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
The nines' complement of a decimal digit is the number that must be added to it to produce 9; the nines' complement of 3 is 6, the nines' complement of 7 is 2, and so on, see table. To form the nines' complement of a larger number, each digit is replaced by its nines' complement.
In set theory, the complement of a set A, often denoted by (or A′), [1] is the set of elements not in A. [ 2 ] When all elements in the universe , i.e. all elements under consideration, are considered to be members of a given set U , the absolute complement of A is the set of elements in U that are not in A .
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.
Once again, the answer can be reached without using the formula by applying the conditions to a hypothetical number of cases. For example, if the factory produces 1,000 items, 200 will be produced by A, 300 by B, and 500 by C. Machine A will produce 5% × 200 = 10 defective items, B 3% × 300 = 9, and C 1% × 500 = 5, for a total of 24.
For example, when or is zero, we can eliminate the associated rows of the coefficient matrix without any changes to the rest of the output vector. If v {\displaystyle v} is null then the above equation for x {\displaystyle x} reduces to x = ( A − 1 + A − 1 B S − 1 C A − 1 ) u {\displaystyle x=\left(A^{-1}+A^{-1}BS^{-1}CA^{-1}\right)u ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".