Ngaahi Vilo Tauʻatāina ʻi he Lulēti
ʻOku kamata ʻa e vilo takitaha mei he ʻikai ha meʻa.
ʻOku ʻikai ha ivi ʻo e ola ʻo ha vilo ʻe taha ki he vilo hoko. Ko e fakafuofua kotoa pē ʻi he uepisaiti ni ʻoku makatuʻunga ʻi he moʻoni ko ia.
Ko e ʻuhinga ʻo e tauʻatāina
p(kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → ʻi he vilo 2 | kulokula ʻi he vilo 1) = p(kulokula) = 18/37. ʻOku ʻikai liliu ha meʻa ʻi hono fakatatau ki he hisitōlia. Ko e ngaahi fika velatui halaFika velaKo ha fika kuo hū lahi ange ʻi he meʻa naʻe ʻamanekina ʻi he taimi siʻi kuo ʻosi. ʻI ha veʻeteka faitotonu ʻoku ʻikai te ne tala ki muʻa ha meʻa.Lau kotoa →, ngaahi fika momokotui halaFika momokoKo ha fika kuo ʻikai hū ʻi ha ngaahi vilo lahi. ʻOku ʻikai ha fakamatala ia ʻe taha ki he ngaahi vilo ʻi he kahaʻu ʻi ha veʻeteka faitotonu.Lau kotoa → mo e ngaahi lanu kuo “taimi” ko ha ngaahi fakamatala ia ʻo e kuohili, ʻo ʻikai ko ha ngaahi tomuʻa tala, pea ʻoku makatuʻunga takitaha ʻi he lau hala ʻoku ʻikai tauʻatāina ʻa e ngaahi vilo lulēti. ʻI he founga fakamatematika, ko e ngalingalimatematikaNgalingaliKo e faingamālie ʻo ha ola, mei he 0 ki he 1 pe 0% ki he 100%. Fika ʻe taha: 1/37 = 2.70%.Lau kotoa → fakataha ʻo ha hokohoko pē ko e fua ia ʻo e fakaliunga ʻo e ngaahi ngalingali ʻo e vilo takitaha, ʻa ia ko e ʻuhinga pē ia ʻoku ngofua ai ʻa e lao fakaliunga ʻi he peesi ʻo e ngalingali.
Ko e hā ʻoku hala fakaesino ai ʻa e “ʻoku ʻikai tauʻatāina ʻa e ngaahi vilo lulēti”
ʻOku lī ʻa e pulumeʻangāuePuluKo e kiʻi pulu siʻisiʻi ʻoku tolongi ʻi he hala ʻo fehangahangai mo e konga vilo. Ko e ngaahi pulu ʻo onopooni ʻoku ngaohi ʻaki ʻa e ivorine pe Teflon, 18–21 mm.Lau kotoa → ʻaki ʻa e nima ʻi ha vave ʻoku kehekehe ʻi he ngaahi vahe hongofulu ʻo e mita ʻi he sekoni; ʻoku ne takai ʻi ha hala ʻoku liliu hono fefaʻuhi ʻo fakatatau ki he efu mo e mamafa ʻo e ʻea; ʻoku ne tā ha taha ʻo e meʻa fakaafemeʻangāueMeʻa fakaafeKo e taha ʻo e ngaahi meʻa ukamea ʻi he konga fakahifo ʻoku nau fakamovetevete ʻa e pulu ʻoku tō. ʻOku toe ui: canoe, diamond, pin.Lau kotoa → ʻe valu ʻi ha tuliki ʻoku fakapapau ʻe he ngaahi meʻa kotoa ko ia; ʻoku ne puna ʻi he ngaahi meʻa vahemeʻangāueMeʻa vaheKo e meʻa vahe ukamea ʻi he vahaʻa ʻo e luo ʻe ua ʻi he veʻeteka.Lau kotoa → ʻa ia ko ʻenau ola ki ha pulu ʻi he 1 m/s ʻoku taʻefakapapau (chaotic) ʻi hono ʻuhinga fakatekinikale. ʻOku ʻikai ha meʻa ʻo e ola kimuʻa ʻoku hao atu ki ha taha ʻo e ngaahi meʻa ko ia. Ko e konga vilomeʻangāueKonga viloKo e konga ʻo e veʻeteka ʻoku vilo pea ʻoku ʻi ai ʻa e ngaahi luo.Lau kotoa → ko e konga vilo tatau pē, ʻa ia ko e feituʻu pē ʻe taha ʻe lava ke toitoi ai ha fakafalala, pea ko e fehuʻi ia ʻo e hehema ʻa e veʻeteka.
Ko e meʻa ʻoku hoko mei ai
Ko e sisitemi peti kotoa pē ko ha fakafuofua ia ʻo e ngaahi ola kuo ʻosi. Kapau ʻoku ʻikai ha fakamatala ʻi he ngaahi ola kuo ʻosi fekauʻaki mo e vilo hoko, ʻoku ʻikai lava ʻe ha fakafuofua pehē ke fakaleleiʻi ʻa e mahuʻinga ʻamanekinamatematikaMahuʻinga ʻamanekinaKo e ola ʻavalisi ʻi he peti takitaha ʻi he taimi lōloa. −1/37 ʻo e peti ki he peti ʻIulope angamaheni kotoa pē.Lau kotoa → ʻo e peti hoko. Ko e faʻahinga fakamatematika ia ʻo e fakakikihi fakafepakiʻi ʻa e ngaahi sisitemi, pea ko e ʻuhinga ia ʻoku lava ai ke tomuʻa tohi ʻa e ngaahi peesi founga ki ha ngaahi sisitemi ʻoku teʻeki fakakaukauʻi: ʻoku ʻikai makatuʻunga ʻa e fakamoʻoni ʻi he lao.
ʻI he taimi ʻe ʻikai ngāue ai
Kapau pē naʻe hehema fakaesino ʻa e veʻeteka pe naʻe lava ke tomuʻa ʻiloʻi ʻa e tukuange ʻa e tīla. Ko e ngaahi kaveinga ia ʻo e Lēpi. Neongo ai, ʻoku fakafalala ki he fisiki, ʻo ʻikai ki he ngaahi ola kuo ʻosi: ko ha luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → hehema ʻoku lahi ange hono ngalingali ʻi he vilo kotoa pē, ʻo ʻikai lahi ange pē hili ʻene “momoko”. Ko e ngaahi fakamatala mei he ngaahi vilo kuo ʻosi ʻe hoko ia ko ha fakamoʻoni fekauʻaki mo e veʻeteka, ʻa ia ko ha meʻa kehe ia mei ha sīpinga ʻi he ngaahi ola.
Ko e tauʻatāina ko ha fakakaukau ʻoku tali
ʻOku ngofua pē ke fakaliunga ʻa e ngaahi faingamālie ʻi he taimi ʻoku tauʻatāina ai ʻa e ngaahi meʻa, pea ʻoku maʻu ʻe ha veʻeteka lulēti ʻa e totonu ko ia ʻi he fisiki. ʻI he ngaahi feituʻu kehe kuo pau ke vakaiʻi. ʻI he 1999 naʻe tukuakiʻi halaia ʻa Sally Clark, ko ha loea ʻIngilani, ʻi hono fakapoongi ʻene ongo foha valevale. Naʻe tala ʻe ha toketā fānau ki he kau sulē ko e faingamālie ke mate fakafokifā ha pēpē ʻe ua ʻi ha fāmili hangē ko hono fāmili ko e 1 ʻi he miliona ʻe 73, ko ha fika naʻa ne maʻu ʻaki hono sikueaʻi ʻa e 1 ʻi he 8,543, ko e faingamālie ʻo e taha. ʻOku lau ʻe he sikueaʻi ʻa e ongo mate ʻo hangē ha vilo ʻe ua ʻo ha veʻeteka. Ka ʻoku vahevahe ʻe he ongo tokoua ʻa e ngaahi siini mo ha ʻapi, ko ia hili ha mate fakafokifā ʻe taha ʻoku lahi ange ʻaupito ʻa e ngalingali ʻo hono ua ʻi he ʻuluaki. Naʻe fakahā ia fakahāhā ʻe he Royal Statistical Society ʻi he 2001, pea naʻe fakataʻeʻaongaʻi ʻa e tukuakiʻi ʻo Clark ʻi ha tangi hono ua ʻi he 2003, hili hono hā mai ʻa e ngaahi fakamoʻoni fakafaitoʻo naʻe ʻikai fakahā. ʻOku ngāueʻaki ʻe Hunacek (2025) ʻa e keisi ke akoʻi ʻaki ʻa e lao ʻoku makatuʻunga ai ʻa e peesi ni: fakaliunga pē ʻa e meʻa ʻoku tauʻatāina.
Tauʻatāina mo e ngaahi tēpile RNG
ʻOku toʻo ʻe he ngaahi tēpile polokalama ʻa e ola takitaha mei ha meʻa ngaohi fika taʻefakataumuʻa kuo fakamoʻoniʻi ʻa ia ʻoku sivi ki he anga totonu ko eni: ko e tauʻatāina fakahokohoko ʻi ha toʻo ʻe laui miliona. Ko e veʻeteka ʻoku ngaue ʻi he sikilini ko ha teuteu pē. Ko ha tēpile RNG ʻoku hā ai ha fakafalala ʻe tō ia ʻi he fakamoʻoniʻi, ʻa ia ko ha sivi mālohi ange ia ʻi ha sivi pē ʻe lava ke fai ʻe ha tokotaha vaʻinga.
Ngaahi fehuʻi
ʻIkai ki ha luo. Mahalo, ʻi ha tuʻunga tatau maʻu pē ʻaupito, ki ha kongaveʻetekaKongaKo ha konga fakavilo hokohoko ʻo e ngaahi luo ʻi he veʻeteka, ʻoku kehe ia mei ha kulupu ʻi he palani ʻo e tēpile.Lau kotoa → ʻo lahi ange ʻi he faingamālie; sio ki he ngaahi fakaʻilonga ʻo e tīla ʻi he Lēpi. ʻOku liliu ʻe he ngaahi sitiutio ʻa e tukuange ke taʻofi ia.
Ki hono vakaiʻi ʻo e hehema ʻi ha vilo ʻe laui afe, ʻi he fakakaukau. Ki he vilo hoko, ʻikai.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
Ko ha peti ʻoku tuku ʻi muʻa ʻi ha vilo ʻe ua ʻoku totongi tatau kapau ʻoku māʻolunga ange ʻa e fika hono ua ʻi he ʻuluaki. ʻOku mole ha tatau, pea ʻoku lau ʻa e 0 ko e fika māʻulalo taha. Ko e hā hono fakamole ʻi ha veʻeteka ʻIulope?
Fakahā ʻa e tali
Tali Ko e 2.70% tofu pē, tatau mo e kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa →.
ʻOku tauʻatāina ʻa e ongo vilo, ko ia ʻoku tatau ʻa e ngalingali ke māʻolunga ange ʻa e fika hono ua ʻi he ʻuluaki mo e ngalingali ke māʻulalo ange. Ko e tuʻunga kehe pē ʻe taha ko ha tatau, ko e fika tatau tuʻo ua, ʻi he ngalingalimatematikaNgalingaliKo e faingamālie ʻo ha ola, mei he 0 ki he 1 pe 0% ki he 100%. Fika ʻe taha: 1/37 = 2.70%.Lau kotoa → ʻo e 1/37.
Ko ia ʻoku ikuna ʻa e peti ʻi he ngalingali ʻo e (1 − 1/37)/2 = 18/37, ko e ngalingali tofu pē ia ʻo e kulokula, pea ʻoku fakamole ʻa e 2.70% tatau.
Kapau naʻe lava ke ke tuku ia hili hoʻo sio ki he ʻuluaki fika ʻe hoko ia ko ha meʻaʻofa: hili ha 0 ʻoku ikuna ia tuʻo 36 ʻi he 37. Ko e ʻuhinga ia kuo pau ai ke tāpuni ha peti pehē ʻi muʻa ʻi he ʻuluaki vilo.
Meʻa fakaoli
ʻOku kamata ʻa e vilo takitaha mei he ʻikai ha meʻa. Ko e fakafuofua kotoa pē heni ʻoku fakafalala ki ai.
Ngaahi Maʻuʻanga
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Hunacek, M. Quantitative Literacy Through Games and Gambling.
- Royal Statistical Society. “Statement regarding statistical issues in the Sally Clark case.”