If Alice collaborates with Paul Erdős on one paper, and with Bob on another, but Bob never collaborates with Erdős himself, then Bob is given an Erdős number of 2, as he is two steps from Erdős.

If Alice measures − x, the system collapses into state IIa, and Bob will get + x.

If Alice knows the true distribution p ( x ), while Bob believes ( has a prior ) that the distribution is q ( x ), then Bob will be more surprised than Alice, on average, upon seeing the value of X.

Alice could send bits to Bob in the following way: If Alice wishes to transmit a " 0 ", she measures the spin of her electron in the z direction, collapsing Bob's state to either or.

If her opponent has a weak hand or is bluffing, Alice expects no further bets or calls from her opponent.

If her opponent has a superior hand, Alice expects the opponent to bet another $ 10 on the end.

* If Alice indicates her result is, Bob knows his qubit is already in the desired state and does nothing.

If Alice has a particle which is entangled with a particle owned by Bob, and Bob teleports it to Carol, then afterwards, Alice's particle is entangled with Carol's.

If each of two hypothetical experimenters, Alice and Bob, has one of the particles that form an entangled pair, and Alice measures the spin of her particle, the measurement will be entirely unpredictable, with a 50 % probability of the spin being up or down.

If Alice then " measures " her half-coin, by opening her envelope, for her the measurement will be unpredictable, with a 50 % probability of her half-coin being " heads " or " tails ", and Bob's " measurement " of his half-coin will always be opposite, hence perfectly anti-correlated.

If in the entangled state given above Alice makes a measurement in the eigenbasis of A, there are two possible outcomes, occurring with equal probability:

If the latter occurs, ( Alice measures 1 ) then Bob's measurement will return 0 with certainty.

:: If Alice wishes to transmit a ' 0 ', she measures the spin of her electron in the z direction, collapsing Bob's state to either | z +>< sub > B </ sub > or | z ->< sub > B </ sub >.

If Alice transmitted a ' 0 ', all his measurements will produce the same result ; otherwise, his measurements will be split evenly between + 1 / 2 and-1 / 2.

If Alice later tripped over the same rock herself, she would be more likely to blame the placement of the rock ( situational ).

If Alice is preferred by more voters then she is the winner of that pairing.

If David calls the $ 5, Alice and Bob only have the option of calling or folding ; neither can raise.

If Alice just has two pair and Ted acts strongly, Alice may think Ted has three fours and fold if she doesn't improve.

If Alice had just bet her hand on the second round, it is likely that Bob would just have called and David may or may not have called, earning Alice $ 2 to $ 4 on the second round.

If a customer wishes a special cut, it will not be available.

If one wishes to discuss a literary figure who uses folklore in his work, the first thing he must realize is that the literary figure is probably part of this ignorant American public.

If not, he was willing to accede to William's wishes in any way that did not block his ultimate aim.

If the sick person wishes to receive the sacrament of penance, it is preferable that the priest make himself available for this during a previous visit ; but if the sick person must confess during the celebration of the sacrament of anointing, this confession replaces the penitential rite A passage of Scripture is read, and the priest may give a brief explanation of the reading, a short litany is said, and the priest lays his hands on the head of the sick person and then says a prayer of thanksgiving over the already blessed oil or, if necessary, blesses the oil himself.

If the player wishes to play the upper 8 ' from the upper manual only and not from the lower manual, a stop handle disengages the jacks labeled A and engages instead an alternative row of jacks called " lute stop " ( not shown in the Figure ).

If a mutual fund investor wishes to redeem his or her investment the fund must be able to meet that request immediately.

If one wishes to employ the notation for a different purpose ( such as denoting open intervals on the real number line ) the ordered pair may be denoted by the variant notation

If the court believes that developments or trends in legal reasoning render the precedent unhelpful, and wishes to evade it and help the law evolve, it may either hold that the precedent is inconsistent with subsequent authority, or that it should be distinguished by some material difference between the facts of the cases.

If the Government wishes to create a comprehensive and robust welfare state, the rate can be increased.

If one is aggrieved by the judicial outcome of an action and wishes to appeal, he may be forever barred from doing so if he fails to meet the deadline by which his appeal may be filed.

If a lawyer wishes to help a client overcome legal obstacles to securing her or his natural rights, he might, for instance, find that assisting in fabricating evidence or committing perjury is more effective than open disobedience.

St Augustine in his City of God writes " God is called omnipotent on account of His doing what He wills " and thus proposes the definition that " Y is omnipotent " means " If Y wishes to do X then Y can and does do X ".

If a rider wishes to stay within normal requirements for higher-level competition, breeches should be white, but beige or another conservative light color is permissible.

On his deathbed, he committed a manuscript to his chaplain, ordering him to consult with Libert Fromondus, a theology professor at Leuven, and Henri Calenus, a canon at the metropolitan church, and to publish the manuscript if they agreed it should be published, adding " If, however, the Holy See wishes any change, I am an obedient son, and I submit to that Church in which I have lived to my dying hour.

" If only I were a fly on the wall ..." is a phrase used when one wishes they could have observed a scene in an omniscient point of view.

" If anyone wishes to write us, let them write directly ," Tatiana wrote to " my dear dove " Chebotareva on 9 December 1917, after expressing concern for fellow nurses and a patient they had once treated together.

If a director or producer wishes, more detailed and elaborate storyboard images are created.

If a town wishes to obtain the title of a city the proper method of procedure is to address a petition to the King through the Home Office.

Echoing Senator Roman Hruska's famous 1970 speech in defense of Harrold Carswell, Coats said to CNN regarding the nomination: " If a great intellectual powerhouse is a qualification to be a member of the court and represent the American people and the wishes of the American people and to interpret the Constitution, then I think we have a court so skewed on the intellectual side that we may not be getting representation of America as a whole.

If the owner wishes to sell the island then the Department has a pre-emptive right.

If the customer wishes to be able to reproduce the photos themselves, they may discuss an alternative contract with the photographer in advance before the pictures are taken, in which a larger up front fee may be paid in exchange for reprint rights passing to the customer.

Villeneuve later remarked that: " If someone said to me that you can have three wishes, my first would have been to get into racing, my second to be in Formula 1, my third to drive for Ferrari ..."