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 ".

Since individuals act according to different probability judgements, these agents ' probabilities are " personal " ( but amenable to objective study ).

Since these high-payoffs have very low probability, a house bias can quite easily be missed unless checking the odds carefully.

Since the probability of a run of five successive heads is only ( one in thirty-two ), a believer in the gambler's fallacy might believe that this next flip is less likely to be heads than to be tails.

Since the probability per distance traveled for a neutron to collide with a nucleus is proportional to the material density, increasing the density of a fissile material can increase k. This concept is utilized in the implosion method for nuclear weapons.

Since a mixed state ρ is a probability distribution over an ensemble, this leads naturally to the definition of the von Neumann entropy:

Since an event of probability 0 should not contribute to the entropy, and given that, the convention is adopted that.

Since the attack, security at many airports worldwide has been escalated, ostensibly to lower the probability of similar events occurring again.

Since is a probability density function for position, we calculate its standard deviation.

Since the number of sex alleles is limited-about 18 are known in Apis-there is a high probability that a queen will mate with one or more drones having sex alleles identical with one of the sex alleles in the queen.

Since the equations dealt with in linear cryptanalysis will vary in probability, they are more accurately referred to as linear approximations.

Since various factors alter the probability of strikes at any given location, repeat lightning strikes have a very low probability ( but are not impossible ).

Since input data fields were in any case frequently built from the output of earlier computer processing, the actual probability of a field containing invalid data was exceedingly low and usually the result of some ' corruption '.

Since this probability is an increasing function of p ( proof via coupling argument ), there must be a critical p ( denoted by p < sub > c </ sub >) below which the probability is always 0 and above which the probability is always 1.

Since the probability of transitioning from state to some state must be 1, this matrix is a right stochastic matrix, so that

Since a multiplication by an orthogonal matrix is a rotation, the theorem says that if the probability distribution of a random vector is unchanged by rotations and the components are independent, then the components are identically distributed and normally distributed.

Since there are hundreds of religions in existence, some having thousands of sects with competing interpretations, the probability that a given person's religion should happen to be the one that is true ( to the exclusion of all others ) is diminishingly small.

Since, as is the case for any probability measure, we have

Since the observer sees a random student, meaning that all students have the same probability of being observed, and the percentage of girls among the students is 40 %, this probability equals 0. 4.

Since < span style =" white-space: nowrap ;"> P ( T ) = P ( T | G ) P ( G ) + P ( T | B < nowiki ></ nowiki >) P ( B < nowiki ></ nowiki >)</ span > ( via the law of total probability ), this is.

Since individual harmonic amplitudes are measured, it is required that the manufacturer disclose the test signal frequency range, level and gain conditions, and number of measurements taken.

Since the sum of the absolute squares of the amplitudes must be constant, must be unitary:

Since the distance between the OLT and ONUs are not uniform, the optical packets received by the OLT may have different amplitudes.

She states: " Since we do not succeed in fleeing it, let us therefore try to look the truth in the face.

Since Johnson's proclamations allowed the Southern states to control the procedure and conduct of their elections in 1865, prominent former Confederate leaders were elected to the U. S. Congress ( but not seated ).

Since Lavoisier's knowledge of strong acids was mainly restricted to oxoacids, such as ( nitric acid ) and ( sulphuric acid ), which tend to contain central atoms in high oxidation states surrounded by oxygen, and since he was not aware of the true composition of the hydrohalic acids ( HF, HCl, HBr, and HI ), he defined acids in terms of their containing oxygen, which in fact he named from Greek words meaning " acid-former " ( from the Greek οξυς ( oxys ) meaning " acid " or " sharp " and γεινομαι ( geinomai ) meaning " engender ").

Since German reunification on 3 October 1990, Berlin has been one of the three city states, together with Hamburg and Bremen, among the present 16 states of Germany.

Since these are a basis, any quantum state of the particle can be expressed as a linear combination ( i. e., quantum superposition ) of these two states:

Since then, a number of Australian states have introduced or tightened importation regulations.

Since many commentators view the notion of sense as identical to the notion of concept, and Frege regards senses as the linguistic representations of states of affairs in the world, it seems to follow that we may understand concepts as the manner in which we grasp the world.

Since 1938, many states have adopted rules similar to the FRCP.

Since poses were chosen to produce the most convincing images of states of mind and psychological conditions, as in Ashes, the figures impart a monumental, static quality.

Since then the Court has appeared to be more open to finding states guilty of torture and has even ruled that since the Convention is a " living instrument ", treatment which it had previously characterised as inhuman or degrading treatment might in future be regarded as torture.

Since about 93 % of the data submitted to the FBI is in this format, the UCR stands out as the publication of choice as most states require law enforcement agencies to submit this data.

Since all the German states except Prussia had joined in the cry against him, he was forced to go to Berlin.

Since Galen states that he is using observations of monkeys ( human dissection was prohibited ) to give an account of what the body looks like, Vesalius could portray himself as using Galen's approach of description of direct observation to create a record of the exact details of the human body, since he worked in a time when human dissection was allowed.

Since real political power belongs to the sole legal party, in certain states under Marxist constitutions of the constitutionally socialist state type inspired by the former Union of Soviet Socialist Republics ( USSR ) and its constitutive Soviet republics, there was no formal office of head of state, but rather the leader of the legislative branch was considered to be the closest common equivalent of a head of state as a natural person.

Since France had been defeated on these two fronts, states previously conquered and controlled by Napoleon saw a good opportunity to strike back.

Since most disagreements over what to include in the constitution were ultimately disputes over the balance of sovereignty between the states and national government, Madison's influence was critical.

Since the Confederacy was founded, among other things, on states ’ rights, one important factor in Davis ’ choice of cabinet members was representation from the various states.

Since there are many different reference ellipsoids the latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that " without the full specification of the coordinate reference system, coordinates ( that is latitude and longitude ) are ambiguous at best and meaningless at worst ".

Since the fall of the Iron Curtain in 1989, unionisation in many eastern European states has collapsed at an even more dramatic rate.

Since slavery had been abolished in Canada in 1833, but was still legal in southern states of the U. S., a Lake Erie crossing was sometimes required for fugitive slaves seeking freedom:

Since this is what ( B ) itself states, it means that ( B ) must be true.

Since mesons are made of one quark and one antiquark, they can be found in triplet and singlet spin states.

Since the end of World War II, many former colonies in the Pacific have become independent states.