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A visual representation of a finite sample space and events. The red oval is the event that a number is odd, and the blue oval is the event that a number is prime. A sample space can be represented visually by a rectangle, with the outcomes of the sample space denoted by points within the rectangle.
In this case, {1,3,5} is the event that the die falls on some odd number. If the results that actually occur fall in a given event, that event is said to have occurred. Probability is a way of assigning every "event" a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2 ...
A campaign to persuade pharmaceutical firms to make all trial data available won its first convert in February 2013 when GlaxoSmithKline became the first to agree. [2] Software used in a trial is generally considered to be proprietary intellectual property and is not available to replicators, further complicating matters.
even though 341 = 11·31 is composite. In fact, 341 is the smallest pseudoprime base 2 (see Figure 1 of [3]). There are only 21853 pseudoprimes base 2 that are less than 2.5 × 10 10 (see page 1005 of [3]). This means that, for n up to 2.5 × 10 10, if 2 n −1 (modulo n) equals 1, then n is prime, unless n is one of these 21853 pseudoprimes.
Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to ...
An integer is even if it is divisible by 2, and odd if it is not. [1] For example, −4, 0, and 82 are even numbers, while −3, 5, 7, and 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201.
Using fast algorithms for modular exponentiation and multiprecision multiplication, the running time of this algorithm is O(k log 2 n log log n) = Õ(k log 2 n), where k is the number of times we test a random a, and n is the value we want to test for primality; see Miller–Rabin primality test for details.
Singly even numbers are those with ν 2 (n) = 1, i.e., integers of the form 4m + 2. Doubly even numbers are those with ν 2 (n) > 1, i.e., integers of the form 4m. In this terminology, a doubly even number may or may not be divisible by 8, so there is no particular terminology for "triply even" numbers in pure math, although it is used in ...