In all probability, the council will screen and endorse candidates for the Assembly and for Congress, and then strive to put its full weight behind these pre-primary favorites.

There is a well-known relationship between probability and entropy which states that Af, where **zq is the probability that state ( i.e., volume for an ideal gas ) could be reached by chance alone.

We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

Strictly speaking, this means that the probability for each possible outcome of the experiment can be computed by multiplying together the probabilities of the possible outcomes of the single binomial trials.

We shall find a formula for the probability of exactly X successes for given values of P and N.

Rather than viewing the abortive recovery in 1959-60 as a reason for believing we have lost prospects for growth '', he said `` it should be viewed as a lesson well learned which will increase the probability of substantial improvement in this recovery ''.

Mr. Philip Toynbee writes, for example, that `` in terms of probability it is surely as likely as not that mutual fear will lead to accidental war in the near future if the present situation continues.

If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify ( in the protocol for the experiment or observational study ) that the responses be transformed to stabilize the variance.

According to Richard Dawkins, a distinction between agnosticism and atheism is unwieldy and depends on how close to zero we are willing to rate the probability of existence for any given god-like entity.

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number n for each orbital became known as an n-sphere in a three dimensional atom and was pictured as the mean energy of the probability cloud of the electron's wave packet which surrounded the atom.

The idea is that the dealer's second card has a fairly high probability ( nearly one-third ) to be ten-valued, giving the dealer blackjack and disappointment for the player.

In computational complexity theory, BPP, which stands for bounded-error probabilistic polynomial time is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of at most 1 / 3 for all instances.

In computational complexity theory, BQP ( bounded error quantum polynomial time ) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1 / 3 for all instances.

In other words, there is an algorithm for a quantum computer ( a quantum algorithm ) that solves the decision problem with high probability and is guaranteed to run in polynomial time.

In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.

Alternatively, for a single system at a well-defined temperature, it gives the probability that the system is in the specified state.

If there are g ( E ) dE states with energy E to E + dE, then the Boltzmann distribution predicts a probability distribution for the energy:

The expression is typically interpreted as the probability amplitude for the state ψ to collapse into the state ϕ.

In quantum mechanics the expression is typically interpreted as the probability amplitude for the state to collapse into the state.

Bayesian probability interprets the concept of probability as " an abstract concept, a quantity that we assign theoretically, for the purpose of representing a state of knowledge, or that we calculate from previously assigned probabilities ," in contrast to interpreting it as a frequency or " propensity " of some phenomenon.

Each die has probability Af of producing an ace ; ;

He used his time in Bourg to research mathematics, producing Considérations sur la théorie mathématique de jeu ( 1802 ; “ Considerations on the Mathematical Theory of Games ”), a treatise on mathematical probability that he sent to the Paris Academy of Sciences in 1803.

Therefore the probability of producing a Set from 3 randomly drawn cards from a complete deck is 1 / 79.

These extra neutrons implied a high probability that a gun-type bomb with plutonium would detonate too early, before a critical mass was formed, scattering the plutonium and producing a small " fizzle " of a nuclear explosion many times smaller than a full explosion.

United States Department of Defense policy explicitly states that non-lethal weapons " shall not be required to have a zero probability of producing fatalities or permanent injuries.

By analogy, if in an alternate universe coins were to behave like photons and other bosons, the probability of producing two heads would indeed be one-third ( tail-head = head-tail ).

P ( D ) should be the probability of producing the data, but on its own is difficult to calculate, so an alternative way to describe this relationship is as one of proportionality:

In any crossing of two carrier parents, there is a 25 % statistical probability of producing a solid-colored, living foal ; a 50 % chance for a frame-patterned, living foal ; and a 25 % chance of a LWS foal.

HYPP is a dominant genetic disorder ; therefore heterozygotes bred to genotypically normal horses have a statistic probability of producing clinically affected offspring 50 % of the time.

The usefulness of a biosignature is determined, not only by the probability of life creating it, but also by the improbability of nonbiological ( abiotic ) processes producing it.

Thus, the tree that has the highest probability of producing the observed data is the most likely tree.

* Dog and cat fanciers may coordinate a breeding program to raise the probability of an animal's litter producing a championship-caliber animal.

) The probability of producing the resonance at a given energy E is proportional to f ( E ), so that a plot of the production rate of the unstable particle as a function of energy traces out the shape of the relativistic Breit – Wigner distribution.

There are costs to producing flowers, since the production of a flower and fruit reduces the probability that the plant will survive, or flower, in following years.

Indeed, it has been proposed that under very mild assumptions ( ergodicity and stationarity ), the probability of producing a sequence that renders language learning impossible is in fact zero.

When an antiproton gets close to a xenon nucleus, an electron-positron pair can be produced, and with some probability the positron will be captured by the antiproton to form antihydrogen.

Section 7 is designed to arrest in its incipiency not only the substantial lessening of competition from the acquisition by one corporation of the whole or any part of the stock of a competing corporation, but also to arrest in their incipiency restraints or monopolies in a relevant market which, as a reasonable probability, appear at the time of suit likely to result from the acquisition by one corporation of all or any part of the stock of any other corporation.

The binomial probability distribution may describe the variation that occurs from one set of trials of such a binomial experiment to another.

More generally, suppose that an experiment consists of a number of independent trials, that each trial results in either a `` success '' or a `` non-success '' ( `` failure '' ), and that the probability of success remains constant from trial to trial.

In this case the stage R operating with conditions Af transforms the state of the stream from Af to Af, but only the probability distribution of Af is known.

Since in practice it is not worth contrasting a zero probability with one that is nearly indistinguishable from zero, he prefers to categorize himself as a " de facto atheist ".

# The electrons are never in a single point location, although the probability of interacting with the electron at a single point can be found from the wave function of the electron.

These are processes which create compound nuclei at low excitation energy (~ 10-20 MeV, hence " cold "), leading to a higher probability of survival from fission.

These are processes which create compound nuclei at high excitation energy (~ 40-50 MeV, hence " hot "), leading to a reduced probability of survival from fission and quasi-fission.

In Bayesian statistics, a probability can be assigned to a hypothesis that can differ from 0 or 1 if the truth value is uncertain.

Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called " inverse probability " ( because it infers backwards from observations to parameters, or from effects to causes ).

In part, the growth was spurred by new connections and applications to other fields, ranging from algebra to probability, from functional analysis to number theory, etc.

Analytic combinatorics concerns the enumeration of combinatorial structures using tools from complex analysis and probability theory.

Pollution can occur from a number of sources: garbage and industrial debris ; the transportation of petroleum in tankers, increasing the probability of large oil spills ; small oil spills created by large and small vessels, which flush bilge water into the ocean.

E. T. Jaynes, from a Bayesian point of view, pointed out probability is a measure of a human's information about the physical world.

The earliest radiocarbon determinations obtained from key sites such as Oakbank in Loch Tay or Redcastle, Beauly Firth approach the Late Bronze Age-Early Iron Age transition at their widest interpretation at 2 sigma or 95. 4 % probability, falling after c. 800BC and therefore could only be considered Late Bronze Age by the narrowest of margins.

The appearance of interference built up from individual photons could seemingly be explained by assuming that a single photon has its own associated wavefront that passes through both slits, and that the single photon will show up on the detector screen according to the net probability values resulting from the co-incidence of the two probability waves coming by way of the two slits.

The probability " wave " can be said to " pass through space " because the probability values that one can compute from its mathematical representation are dependent on time.