Dambudziko: Vhiri reZuva reKuberekwa
Kutenderera kungani kunodiwa kuti imwe nhamba idzokororwe? Kushoma zvikuru pane zvinofungidzirwa nevanhu vazhinji.
Dambudziko rezuva rekuberekwa pavhiri rine makombamidziyoGombaImwe yemakamuri 37 ane nhamba parotor. Mamwe mazita: slot, cup.Verengai zvese → 37: mushure mekutenderera 8 chete pane mukana unopfuura hafu kuti imwe nhamba yatobuda kaviri. Vatambi vanoverenga kudzokororwa semaitiro; ndiwo maitiro anotarisirwa evhiri rakaenzana.
Dambudziko
Tenderedzai vhiri reEurope rakaenzana. Kutenderera kungani kusvika mukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → wekuti kutenderera kuviri zvishoma kwaratidza nhamba imwe chete wapfuura hafu? Vatambi vazhinji vanofungidzira 18 kana 19, hafu ye37. Mhinduro i8.
Mhinduro
Verengai mukana wekusadzokororwa mobvisa paimwe. Mushure mekutenderera k, p(dzese dzakasiyana) = (37/37)(36/37)(35/37)…((38 − k)/37). Pa k = 8: 1 × 0.973 × 0.946 × 0.919 × 0.892 × 0.865 × 0.838 × 0.811 ≈ 0.44, saka p(kumwe kudzokororwa) ≈ 0.56. Pa k = 14 i0.93; pa k = 20 i0.996. Pfungwa dzinokanganisa nekuti huwandu hwemapeya ekutenderera hunokura se k², uye peya ipi neipi inogona kuenderana.
Sei zvakakosha patafura
Bhodhi remhedzisiro rinoratidza nhamba 20 dzekupedzisira richaratidza kudzokororwa kumwe zvishoma nguva dzinenge dzese, kazhinji kuviri kana kutatu. Vatambi vanoona “17 yabuda kaviri mukutenderera gumi” vobva vati 17 inopisa; masvomhu ezuva rekuberekwa anoti kudzokororwa mukati mekutenderera gumi kunoitika 74% yenguva uye nhamba yakadzokororwa haina hurongwa. Maitiro aya ndeechokwadi; chirevo hachisi.
Dambudziko rinotevera
Kutenderera kungani kusvika nhamba yakatarwa, semuenzaniso 17, yabuda kaviri? Uyu mubvunzo wakasiyana une mhinduro huru zvikuru: kumirira kunotarisirwa ikutenderera 74, uye mukana we17 mbiri mukati mekutenderera 20 unenge 10%. Musiyano pakati pe“imwe nhamba inodzokororwa” (kutenderera 8) ne“nhamba iyi inodzokororwa” (kutenderera 74) ndiwo musiyano wose pakati pemaitiro amunoona gare gare nekufanotaura kwamunoita pachine nguva.
Edzai
Mhanyisai Mutambo weDemo kutenderera gumi motarisa nhoroondo. Kazhinji pachava nekudzokororwa. Mhanyisai zvakare. Nhamba yakadzokororwa ichava yakasiyana. Itai izvi kagumi uye maona dambudziko rezuva rekuberekwamasvomhuDambudziko rezuva rekuberekwaVanhu vangani vanodiwa kuti vaviri vangangova nezuva rimwe chete rekuberekwa, kana kuti kutenderera kungani kunodiwa kuti nhamba ingangodzokororwa. Pavhiri remakomba 37, kutenderera 8 kunokwana kuti mukana upfuure hafu.Verengai zvese →; itai kane chiuru (masimulator anogona) uye maripima.
Fomula
Mibvunzo
Chaizvo, nemakomba 37 pane mazuva 365. Vanhu 23 vanopa 50% pamazuva ekuberekwa; kutenderera 8 kunopa 56% pavhiri.
50% mushure mekutenderera kunenge 19. Zvichiri zvakajairika.
Kwete. Kutenderera kwezviuru kubva pavhiri rimwe kungaratidza; kudzokororwa hakumboratidzi.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
Bhodhi remhedzisiro riri padivi pevhiri reAmerica rinoratidza kutenderera 16 kwekupedzisira. Mukana wakadii wekuti hapana nhamba inooneka kaviri pariri?
Ratidza mhinduro
Mhinduro Anenge 2.5%: angangoita mabhodhi 39 pa40 anoratidza kanenge kudzokororwa kumwe.
Endai kutenderera nekutenderera. Kutenderera kwekutanga kunogona kuva chero chii. Kwechipiri kunofanira kuipotsa: mikana 37 pa38. Kwechitatu kunofanira kupotsa dzose mbiri: 36 pa38. Kwechigumi nematanhatu kunofanira kupotsa nhamba gumi neshanu: 23 pa38.
Wanzai: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0.0246.
Bhodhi risina kudzokororwa ndiro risingawanzoitika. Bhodhi rine kudzokororwa haritauri chinhu nezvevhiri.
Pakutenderera gumi kwevhiri reEurope, mukana wakadii wekuti 17 ibude kashanu chaiko? Wekuti imwe nhamba, chero nhamba, ibude kashanu kana kupfuura? Uye wekuti imwe nhamba ibude kanenge katatu pakutenderera kuna?
Ratidza mhinduro
Mhinduro 17 kashanu chaiko: 1 pa315,576. Imwe nhamba kashanu kana kupfuura: anenge 1 pa8,333. Imwe nhamba katatu kana kupfuura pakutenderera kuna: 1 pa349.
17 kashanu: sarudzai kuti kutenderera kupi kushanu pagumi, nzira 252, imwe neimwe ine mukana we(1/37)⁵ × (36/37)⁵. Pamwe chete, 1 pa315,576.
Imwe nhamba: nhamba yega yega pa37 ine mukana we1 pa308,325 wekubuda kashanu kana kupfuura, izvo zvinopa 37 pa308,325, kana 1 pa8,333. Chiitiko chisingawanzoitiki chenhamba mbiri dzinobuda kashanu imwe neimwe chinoverengwa kaviri, asi kuchibvisa hakuchinji chinhu pakururama uku.
Katatu pakutenderera kuna: panhamba imwe, 4 × 36 + 1 = 145 pamhedzisiro 37⁴ inogoneka; panhamba ipi neipi pa37, 145/37³ = 1 pa349.
Pavhiri rine zerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → mbiri, nhamba dzakafanana ndi1 pa359,275, 1 pa9,243 ne1 pa368. Musiyano uri pakati pe“17” ne“imwe nhamba” idambudziko rezuva rekuberekwamasvomhuDambudziko rezuva rekuberekwaVanhu vangani vanodiwa kuti vaviri vangangova nezuva rimwe chete rekuberekwa, kana kuti kutenderera kungani kunodiwa kuti nhamba ingangodzokororwa. Pavhiri remakomba 37, kutenderera 8 kunokwana kuti mukana upfuure hafu.Verengai zvese → zvakare: kune nzira 37 dzekushamiswa.
Kuseka zvishoma
Chimwe chinhu chinodzokororwa nekukurumidza. Chinhu ichocho hachina hurongwa.
Zvinyorwa
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, roulette questions.