Given uniformly randomly chosen x on the interval (1,5) and y on the interval (1,5) find the probability of each:

[x] + [y] = [x+y]

[x] - [y] = [x-y]

[x] * [y] = [x*y]

[x] / [y] = [x/y]

Where [x] is the floor function, the greatest integer less than or equal to x.

(In reply to re: solutions for first three by Jer)

For what it's worth, using more extended precision, the natural antilog of the answer for the multiplicative case is

 1.12687923324455540268936669324337150838499999961844677230206692793398728202997
41535294787955622960758032680537531429918446249598941175135446743989418938998572
98073254014332221936988529429069292509758169742221091318088210976283401344642549
79913672123717489134258556710606565537810792346840610747992796128317576688268455
38375105138603539026832307902282920692547323986090683945337610818071681826373509
87343610927628752636892955278108391147871077931249189156674021015436191782794964
05700749991676190583319225615381005673838611336770668599542659547559642478372715
61147527025487131379988932384002965742534745726471229049611584657803485970246475
31604916227994181675358194098637091542667436160573996927909055168448126334661978
62107272262237283604970141717214267830927008657301861899266807691444737910433966
18437705707229501029427140473808228223255872671825253413647417271213184795416046
17437285638727284998491531615630469162165116859687404915981030732708716176904729
47896693223556239452447016892993421255225652244656870973260835820825278333606105
61517557096403999853038630479842821684850598657409578823120497111605754079721282
94331445339806874264041391225025064924664696263278915386296612190116243786458882
6579007

It doesn't seem to have begun repeating.

Posted by Charlie on 2007-05-18 14:56:25