When three dice are tossed repeatedly, what is the probability that the number of aces is 0 ( or 1, or 2, or 3 )??

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

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.

When the probability of different events is not independent, the probability of future events can change based on the outcome of past events ( see statistical permutation ).

When the probability of repeated events are not known, outcomes may not be equally probable.

When we perform the experiment, the probability of obtaining two particles in the state is now 0. 33 ; the probability of obtaining two particles in the state is 0. 33 ; and the probability of obtaining one particle in the state and the other in the state is 0. 33.

When a coin is fair, that is, the probability of heads is the same as the probability of tails, the entropy of a coin toss is as high as it could be.

When is a conditional probability distribution and the loss function is the negative log likelihood:, then empirical risk minimization is equivalent to maximum likelihood estimation.

When either randomness or uncertainty modeled by probability theory is attributed to such errors, they are " errors " in the sense in which that term is used in statistics ; see errors and residuals in statistics.

When dealing with experiments that are random and well-defined in a purely theoretical setting ( like tossing a fair coin ), probabilities describe the statistical number of outcomes considered divided by the number of all outcomes ( tossing a fair coin twice will yield HH with probability 1 / 4, because the four outcomes HH, HT, TH and TT are possible ).

When it comes to practical application, however, the word probability does not have a singular direct definition.

When studying axiomatic probability theory, many deep consequences follow from merely these three axioms.

When we measure this qubit in the standard basis, the probability of outcome is and the probability of outcome is.

When a statistical procedure has been specified in the study protocol, then statistical theory provides well-defined probability statements for the method when applied to all populations that could have arisen from the randomization used to generate the data.

When the stereochemistry of a macromolecule is considered to be a Bernoulli process, triad composition can be calculated from the probability of finding meso diads ( P < sub > m </ sub >).

When we consider 100 billion monkeys, the probability falls to 0. 17 %, and as the number of monkeys n increases, the value of X < sub > n </ sub > – the probability of the monkeys failing to reproduce the given text – approaches zero arbitrarily closely.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

When they express themselves it is incandescent hatred that shines forth, the rage of repudiation, the ecstasy of negation.

When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.

When the proprietor dies, the establishment should become a corporation until it is either acquired by another proprietor or the government decides to drop it.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When I take over Taliesin, the first thing I'll do is fire you ''.

When someone in the audience rose and asked how does it feel to be a celebrity, Carl said, `` A celebrity is a fellow who eats celery with celerity ''.

When decision makers act within this frame they determine whether a claim put forward in the name of religion is to be accepted by the larger community as appropriate to religion.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When we turn to Aristotle's ideas on the moral measure of literature, it is at once apparent that he is at times equally concerned about the influence of the art.

When their faith in civil liberties is tested against strong pressures of social expediency in specific issues, e.g., suppression of `` dangerous ideas '', many waver and give in.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

When I first came across Samuel Johnson's pronouncement, `` the remedy for the ills of life is palliative rather than radical '', it seemed to me to sum up the profoundest of political and social truths.

When all else fails, it is argued that open sessions slow down governmental operations.

When a person has thoughtlessly or deliberately caused us pain or hardship it is not always easy to say, `` Just forget it ''.

When a person meets God's requirements for the experience of forgiveness he is forgiven.

When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When we become firm enough to stand for those ideals which we know to be right, when we become hard enough to refuse to aid nations which do not permit self-determination, when we become strong enough to resist any more drifts towards socialism in our own Nation, when we recognize that our enemy is Communism not war, and when we realize that concessions to Communists do not insure peace or freedom, then, and only then will we no longer be `` soft ''.

When one powerful nation strives to emulate the success of another, it is only natural.

When a man is laid to rest, he is entitled to stay put.

When I talked to Ching about it, he said, Everyone can learn, if he is not a Reactionary or lazy.

When Af for each i, we shall have Af, because the operator Af will then be 0 on the range of Af.

When the functions J < sub > n </ sub >( x ) are plotted on the same graph, though, none of the zeros seem to coincide for different values of n except for the zero at x = 0.

The island of Sal receives an average of 0. 0mm in May, When the rain come, if it comes, can be very strong.

When U and V are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio U / V has the standard Cauchy distribution.

When Newton's method is used to find the solution for the maximum likelihood estimate, the middle 24 % order statistics can be used as an initial solution for x < sub > 0 </ sub >.

When b is zero and A ≠ 0 the origin is an equilibrium ( or singular ) point of the flow, that is, if x < sub > 0 </ sub > = 0, then the orbit remains there.

When b = 0, the eigenvalues of A determine the structure of the phase space.

When the eigenvalues of J are not in the unit circle, the dynamics near the fixed point x < sub > 0 </ sub > of F is called hyperbolic and when the eigenvalues are on the unit circle and complex, the dynamics is called elliptic.

When the eccentricity is 0 the foci coincide with the center point and the figure is a circle.

When n > 0, it can be shown that

When Freenet 0. 5 ( FCon or Freenet Classic Opennet ) forked into Freenet 0. 7, most users moved to Freenet 0. 7.

When that interval is 0. 5 / T, the applicable reconstruction formula is the Whittaker – Shannon interpolation formula.

When the World Cup began, Banks was in goal as England got through their group containing Uruguay, Mexico and France, drawing 0 – 0 with the former and clinching 2 – 0 victories over the latter.

When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak König's lemma, with the equivalence provable in RCA < sub > 0 </ sub > ( a second-order variant of Peano arithmetic restricted to induction over Σ < sup > 0 </ sup >< sub style =" margin-left :- 0. 6em "> 1 </ sub > formulas ).

When people are asked to make up a random-looking sequence of coin tosses, they tend to make sequences where the proportion of heads to tails stays closer to 0. 5 in any short segment than would be predicted by chance ( insensitivity to sample size ); Kahneman and Tversky interpret this to mean that people believe short sequences of random events should be representative of longer ones.

When inspired air contains CO levels as low as 0. 02 %, headache and nausea occur ; if the CO concentration is increased to 0. 1 %, unconsciousness will follow.