PROBABILITY 



6'345 



PROBOSCIS MONKEY 



attempt to solve problems of 

 chance was made by Fermat and 

 Pascal in 1654, when they found 

 what would be the final scores in 

 an unfinished game of cards be- 

 tween two players of equal skill. 

 Leibniz established the funda- 

 mental principles of the calculus of 

 probabilities, and Cotes, a con- 

 temporary of Newton, wrote on a 

 method of determining the most 

 probable results from a number of 

 observations. Demoivre, La- 

 grange, Laplace, and other leading 

 mathematicians placed the theory 

 on firm foundations. 



The fundamental principle in 

 probabilities is simply stated by 

 Todhunter in his algebra as fol- 

 lows : If an event may happen in 

 a ways and fail in b ways and all 

 these ways are equally likely to 

 occur, the probability of its hap- 

 pening is a / (a -\-b) and the proba- 

 bility of its failing is b / (a-\-b). 

 Furthermore, if there are any 

 number of events A, B, C, etc., 

 such that one must happen and 

 only can happen, and suppose 

 a,b,c, etc., to be the number of 

 ways in which these events can 

 respectively happen, then the pro- 

 babilities of the events are pro- 

 portional to a, b, c, etc., respec- 

 tively. If, for example, there are 

 three events, then A can happen 

 in a ways out of a-\-b-{-c ways and 

 can fail in b-\-c ways. Therefore 

 the probability of A's happening is 

 a I (a-f-6-J-c) ways, and of its 

 failing (b+c) / (a+6+c) ways, 

 and so on for the other events. 



As simple examples in the theory 

 of probabilities the probability of 

 drawing a white ball from a bag 

 containing 7 white balls and 8 

 black balls is 7/15, and the pro- 

 bability of throwing an ace first 

 time with a die is 1/6. See History 

 of the Theory of Probabilities, I. 

 Todhunter, 1865. 



Probability (Lat. probabili*, 

 capable of being proved). The 

 likelihood of a statement or event 

 being realized, the degree of confi- 

 dence in its realization according 

 to what we know at the moment. 

 The term occupies an intermediate 

 position between certainty and 

 doubt. But whereas doubt is al- 

 ways subjective (referring to state 

 of mind), and certainty sometimes 

 objective and sometimes subjec- 

 tive, probability is always objec- 

 tive, . indicating the character of 

 things or of our judgements upon 

 them. Probability may be calcu- 

 lated a priori (q.v.), from the 

 nature of the case (as in games of 

 chance), or by actually counting 

 the number of instances. 



Probate (Lat. probatum, some- 

 thing proved). Official proof of the 

 legality of a will. In English law, 



derived in this respect from eccle- 

 siastical law, it is necessary for the 

 will of a deceased person to be 

 proved in the probate division of 

 the high court of justice before it 

 can be acted upon. That is, the 

 judge or other officer of the court 

 must be satisfied by proof that the 

 document in question is really the 

 will of the deceased. In the case of 

 a will which appears to have been 

 duly executed, and to which there 

 is no opposition, the officials of the 

 probate registry grant probate 

 without trouble ; but when there 

 appears to be some irregularity in 

 the execution of the will, or there 

 is opposition by anyone interested, 

 the matter comes before a judge in 

 court. Probate can be granted by 

 any officer of inland revenue in 

 cases where the personal estate 

 does not exceed 300. 



When the will is admitted to 

 probate, the original will is filed in 

 Somerset House, and is a public 

 document which can be inspected 

 by anybody on payment of a small 

 fee. The officials then make a 

 copy on parchment, which is called 

 the probate copy, and it is this 

 (pommonly called " the probate ") 

 which is always used, and is ad- 

 mitted everywhere as evidence of 

 the will. In addition to the prin- 

 cipal registry in London, the Court 

 of Probate Act of 1857 set up 40 

 district registries throughout the 

 country, where original wills proved 

 locally are kept and are similarly 

 available for inspection. When- 

 ever a deceased person has pro- 

 perty in England, his will must be 

 proved in the probate registry, 

 otherwise that property cannot be 

 dealt with. See Administrator ; 

 Estate Duty ; Executor ; Will. 



Probation. System in vogue in 

 criminal courts for releasing delin- 

 quents without punishment during 

 good behaviour. 



In its beginnings in Great Britain 

 the movement was not wholly suc- 

 cessful. The Probation of First 



Proboscis Monkey of Borneo 



Offenders Act, 1887, was restricted 

 in scope, and provided no means of 

 making probation really effective. 

 Such means were first sought in the 

 American courts, where probation 

 officers were appointed to supervise 

 offenders during their time of test- 

 ing. So fruitful did the experiment 

 prove that its methods were applied 

 in the United Kingdom by the 

 Probation of Offenders Act, 1907, 



The measure gives discretion to 

 judges and magistrates to release 

 a prisoner on probation, instead of 

 sentencing him straightway, when- 

 ever " the character, antecedents, 

 age, health, or mental condition of 

 the person charged," the trivial 

 nature of his offence, or extenuat- 

 ing circumstances, warrant such 

 leniency. He is bound over to be 

 of good behaviour and to appear 

 for sentence, if called upon, during 

 a period not exceeding three years ; 

 and, if such a course seems ad- 

 visable, he is placed under the care 

 of a probation officer. 



In dealing with young offenders, 

 and with others who have been led 

 into crime by sudden temptation, 

 weakness of character, or adverse 

 home conditions, the surveillance 

 of a kind but firm officer proves in- 

 valuable. Should his charges, how- 

 ever, neglect this chance of reform- 

 ation, the law is again invoked ; 

 they are recalled and sentenced for 

 the original offence. See Borstal Sys- 

 tem; Criminology; Reformatory. 



Probationer (Lat. probatio, 

 test). Term applied to one under- 

 going trial for membership of a 

 Church or other religious com- 

 munity ; for election or call to a 

 pastorate ; or for admission to a 

 profession, such as nursing. In 

 Scotland, a divinity student ad- 

 mitted by a presbytery to trial as a 

 preacher before ordination is called 

 a probationer. See Presbyterianism. 



Problem. Generally, any ques- 

 tion for discussion and settlement. 

 In geometry, it is a proposition in 

 which some operation or construc- 

 tion is required, e.g. to construct a 

 triangle on a given straight line 

 equal in area to a given triangle. 

 The most famous problem is that 

 of the three bodies moving under 

 the sole influence of their mutual 

 attractions. The problem is soluble 

 only for particular cases, and the 

 general problem has defied solution 

 by mathematicians. It is one of 

 great importance in astronomy, 

 and its solution would auto- 

 matically solve many other pro- 

 blems of the solar system. 



Proboscis Monkey (Nasal is 

 larvatus). Species of monkey, 

 found only in Borneo. It is distin- 

 guished by its long and bulbous 

 nose, which in the adult male hangs 

 down and conceals most of the 



