2022.03.13.
self loading rifles Cei-Rigotti (made in Italy) and rifles Carcano M91 Carbine (made in Italy)
What is the probability of the "Italian" week (double made in Italy)?
my calculations 🙂
The "Italian" set has 7 elements: Cei-Rigotti, Carcano M91 Carbine, Automatico M1918, Perino Model 1908, Vetterli-Vitali M1870/87, Modello 1915 Pistol, Bodeo 1889 Revolver.
The "International" set has 69 elements: Model 1900, Model 10, M1897 Shotgun, Sjögren Inertial Shotgun, 12G automatic, Ribeyrolles 1918 Carbine, Hellriegel 1915, SMG 08/18, Annihilator, MP18, Automatico M1918, RSC SMG, M1917 Trench Carbine, Maschinenpistole M1912/P.16, Farquhar-Hill, Mondragon, RSC 1917, Selbstlader M1916, General Liu, Howell Automatic, M1907 Selfloading, Fedorov Avtomat, Cei-Rigotti, Model 8 Autoloading, Selbstlader 1906, Chauchat, Parabellum MG14/17, Lewis gun, LMG 08/18, M1917 MG, MG15 N.A, BAR M1918, Madsen MG, Perino Model 1908, Huot Automatic Rifle, M1909 Benet Mercie, Lebel Model 1886, Mosin-Nagant M91, SMLE MKIII, Martini Henry, Ross MKIII, Gewehr M.95, M1903, Vetterli-Vitali M1870/87, M1917 Enfield, Gewehr 98, Type 38 Arisaka, Russian 1895, Carcano M91 Carbine, P08 Pistol, British Bulldog, Frommer Stop, Auto revolver, Nagant Revolver, Mars Automatic Pistol, 1903 Hammerless, C-93 Pistol, Repetierpistole M1912, Revolver MK VI, C96 Pistol, M1911 Pistol, NO. 3 Revolver, Howdah pistol, MLE 1903 pistol, Bodeo 1889 Revolver, Modello 1915 Pistol, Obrez pistol, M1914 Taschenpistol, Kolibri pistol, Gasser M1870 Revolver.
If the set has n elements, the number of k-combinations, denoted by C(n, k) is equal to n! / (k! (n-k)! ).
The "Italian" set has 7 elements, the number of 2-combinations, denoted by Italian(7, 2) is equal to 7! / (2! 5! ) = 21.
The "International" set has 69 elements, the number of 2-combinations, denoted by International(69, 2) is equal to 69! / (2! 67! ) = 2346.
The probability of the "Italian" week is equal to Italian(7, 2) / International(69, 2) = 21 / 2346 = 0.00895140664
And the probability of the "Sjögren Inertial Shotgun" week is equal to NoSjögren(68, 1) / International(69, 2) = 68 / 2346 = 0.02898550724
The probability of the "Sjögren Inertial Shotgun" week is three times the probability of the "Italian" week (68 / 21 = 3.2380952381).
according to my calculations 🙂