There must not only be greater good than evil objectively in view, but also greater probability of actually doing more good than harm.

If others expect that you'll reward them for doing what you want, there's a high probability that they'll do it.

This is because doing an average this way simply computes the proportion of successes seen, which we expect to converge to the underlying probability of success.

* Mathematics — Writing: Approximately 10 < sup >− 183, 800 </ sup > is a rough first estimate of the probability that a monkey, placed in front of a typewriter and given adequate food, breaks, and sleep while doing so, will type all the letters of Hamlet on the first try.

Performing nonprobability sampling is considerably less expensive than doing probability sampling, but the results are of limited value.

The probability of doing so in two draws would depend on whether the first card drawn were replaced before the second drawing, since without replacement there would be one fewer card after the first card was drawn.

In doing so, when a female eider left the nest after laying the first egg, the probability that the predator attacked her egg decreased on account of presence of others ’ eggs.

The judge directed the jury that they could infer intention if there was a high degree of probability that the victim would be killed and if the defendants knew " quite well that in doing that there was a high degree of probability " that the victim would be killed.

On the other hand, TKKG frequently act at the border of probability, and Kalmuczak is forced to create genuine role models for the readers in TKKG, and in doing so, by course, makes the storyline absurd ; TKKG become caricatures.

Sample areas in the new investigations were selected strictly by application of the principles of probability theory, so as to be representative of the total population of defined areas within calculable limits.

When more electrons are added to a single atom, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection ( sometimes termed the atom ’ s “ electron cloud ” ) tends toward a generally spherical zone of probability describing where the atom ’ s electrons will be found.

Even so, its kill rate was only 13 % in combat in 1972, leading to a practice of ripple-firing all four at once in hopes of increasing kill probability.

* For the frequentist a hypothesis is a proposition ( which must be either true or false ), so that the frequentist probability of a hypothesis is either one or zero.

Intuitively, it is the " area so far " function of the probability distribution.

However, if clusters are selected with probability proportionate to size, the same number of interviews should be carried out in each sampled cluster so that each unit sampled has the same probability of selection.

The probability measure on Cantor space, sometimes called the fair-coin measure, is defined so that for any binary string x the set of sequences that begin with x has measure 2 < sup >-| x |</ sup >.

Given the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.

If it is " observed " ( measured with a photon ) not at a particular slit but rather at the screen, then there is no " which path " information as part of the interaction, so the electron's " observed " position on the screen is determined strictly by its probability function.

μ is a finite measure on the sigma-algebra, so that the triplet ( X, Σ, μ ) is a probability space.

Suppose random variable X can take value x < sub > 1 </ sub > with probability p < sub > 1 </ sub >, value x < sub > 2 </ sub > with probability p < sub > 2 </ sub >, and so on, up to value x < sub > k </ sub > with probability p < sub > k </ sub >.

In the classical interpretation, probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, e. g. the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube.

Fundamental analysis lets them find ' good ' companies, so they lower their risk and probability of wipe-out.

Our research, however, demonstrates that when study participants are placed in real, rather than hypothetical, bargaining situations and are presented with accurate information regarding their statistical probability of success, just as they might be so informed by their attorney or the government during a criminal plea negotiation, innocent defendants are highly risk-averse.

Bayesian methods would suggest that one hypothesis was more probable than the other, but individual Bayesians might differ about which was the more probable and by how much, by virtue of having used different priors ; but that's the same thing as disagreeing on significance levels, except significance levels are just an ad hoc device which are not really a probability, while priors are not only justified by the rules of probability, but there is definitely a normative methodology to define beliefs ; so even if a Bayesian wanted to express complete ignorance ( as a frequentist claims to do but does it wrong ), they could do it with the maximum entropy principle.

The likelihood of other possibilities do not need to be eliminated altogether but they must be so reduced that the greater probability lies with the defendant.

* a confidence interval ( or set estimate ); i. e., an interval constructed using a dataset drawn from a population so that, under repeated sampling of such datasets, such intervals would contain the true parameter value with the probability at the stated confidence level,

To the player it might appear that a winning symbol was ' so close ', whereas in fact the probability is much lower.

In all probability it was not a distinction that Mill was particularly trying to make and so the evidence in his writing is inevitably mixed.

Repeated motions must be " so devoid of merit and be so frivolous that they can be described as a flagrant abuse of the system, have no reasonable probability of success, lack reasonable or probable cause or excuse, and are clearly meant to abuse the processes of the courts and to harass the adverse party than other litigants.

The sampling program was instituted before the principles of probability sampling were widely recognized in population studies.

Max Born suggested that the electron's position needed to be described by a probability distribution which was connected with finding the electron at some point in the wave-function which described its associated wave packet.

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 general consensus in the scientific community, however, was to associate this type of complexity with Kolmogorov, who was concerned with randomness of a sequence, while Algorithmic Probability became associated with Solomonoff, who focused on prediction using his invention of the universal a priori probability distribution.

Further investigation and theoretical work showed that the effect was a radiationless effect more than an internal conversion effect by use of elementary quantum mechanics and transition rate and transition probability calculations.

The P < small >< sub > k </ sub ></ small > ( kill probability ) of the AIM-7E was less than 10 %; US fighter pilots shot down 55 aircraft using the Sparrow.

It was used to good advantage in the 1991 Gulf War, where it scored many USAF air-to-air kills ; its kill probability, overall, is still less than 40 %.

Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

Nevertheless, it was the French mathematician Pierre-Simon Laplace, who pioneered and popularised what is now called Bayesian probability.

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 ).

After the 1920s, " inverse probability " was largely supplanted by a collection of methods that came to be called frequentist statistics.

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.

Full-automatic fire was also considered a desirable feature, allowing the soldier to fire short bursts of three to five rounds, increasing the probability of a hit on a moving target.

More exciting for planetary astronomers was that the best orbital solutions suggested that the comet would pass within of the center of Jupiter, a distance smaller than the planet's radius, meaning that there was an extremely high probability that SL9 would collide with Jupiter in July 1994.

As a greater weight of man and armor could be supported in the saddle, the probability of being dismounted in combat was significantly reduced.

However, due to Eisenhower's persistence, the pivotal supply port at Antwerp was successfully, albeit belatedly, opened in late 1944, and victory became a more distinct probability.

The Etruscan alphabet employs a Euboean variant of the Greek alphabet using the letter digamma and was in all probability transmitted through Pithecusae and Cumae, two Euboean settlements in southern Italy.

The formula was derived by Agner Krarup Erlang and is not limited to telephone networks, since it describes a probability in a queuing system ( albeit a special case with a number of servers but no buffer spaces for incoming calls to wait for a free server ).

) This result was extended in 1987 to show that the probability that k random integers has greatest common divisor d is d < sup >- k </ sup >/ ζ ( k ).

It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson.

An upper limit of 750 BC is indicated by a number of considerations, such as the probability that his work was written down, the fact that he mentions a sanctuary at Delphi that was of little national significance before c. 750 BC ( Theogony l. 499 ), and he lists rivers that flow into the Euxine, a region explored and developed by Greek colonists beginning in the 8th century BC.