The Answer To the Editor of the '"NowTl-CuiNa Datty News."
'Sin,—Before an attempt may be made' to settle, the controversy. between "Pascal" and his friend, it appears necessary to get a clear! dea of what your correspondent exactly means. by the "certain maxinium" to which he refers.
Meanwhile, this much may be Regarding the wheel—as al" presumably does—as consisting of 36 equal and alternate Sectors (18 red-18 black, each of which has an equal deal case, but any other treat-of the subject would require specific assumptions as to the mechanical particularities of the wheel). The probability of di ing red r times i'm repeated trials dependent events) i where stands ions of n objects taken y at a and, equals ni/e! (ner)!
'The probability of obtaining any particular result—say, for instance, 45 red and 55 black therefore: depends exclusively on the number of trials " and probability p in any' one trial but not on the mumber of sectors on the wheel, as Tong s all have an equal chance to ive drawn in any one trial, Such 'a case, p remains constantly equal to 1/2, Of all possible results the most probable one is up. times red (here 80 red-50 black) but the probability fof its happening is not more than 0.0798 (approximately). Any other particular result is, however, stilt Hess probable. (The probability of having 45 red and 55 black is 0.0486).
Now, {t may be that your corre spondent had in mind the deviation from the most probable result, The: probability that thi deviation will hot exceed riy given number. x most probable result) integral and where y: x//@761=P) Here again the probability is seen to depend. on. the number of trials bility in each trial but, the latter remains con:
assumed here, the proba bility' is independent of the number sectors.
This of course holds good for what known as the "probable" deviation <which is. perhaps what "Pascal alluding to when he refers to a "certain maximum", fe.: the devtawill find sometimes even among the! intelligent class of people indi duals, who are baffled when confront-_ ted with above query. Moreover, I have just recently stumbled over a friend of mine, otherwise a highly educated and clever man, who even argues the point that we can see from our Earth always only. one fal? (avays the same half) of the 'When I consider some very exeellent articles and clever letters sent} in by your correspondents, I feel almost ashamed to ask you' to pul Tish this query. "However, in. order to satisfy my unbelieving friend, T'ventare to have this controversy published, if it is not abusing the hospitality of your columns, even at the risk that this query will be! found. silly and ridiculous.
Text read from the printed page and cleaned; old type leaves the occasional error.