Te Tūponotanga i te Rūreti
Ko ia tūponotanga o te rūreti he tatau kōhao kua wehea ki te 37.
p = ngā tau ka kapi / 37. Kotahi te tau: 2.70%. Tekau mā waru: 48.65%. Ko te tūpono o tētahi raupapa motuhake ka whakareatia ngā tūponotanga o ia hurihanga kotahi.
Ngā hurihanga kotahi
He ōrite te tūpono o ia kōhaotaputapuKōhaoTētahi o ngā wehenga e 37 kua tauia i te rōta. Arā anō: slot, cup.Pānuitia katoatia → o ngā kōhao 37, nō reira ko te tūpono ki te toa i te rūreti i te hurihanga kotahi he mahi tatau noa iho. Ka toa te peti ki ngā tau e whā i te 4/37 o ngā wā, tata ki te 10.8%. Kāore he mea anō i tua atu i tērā i roto i te tūponotangapāngarauTūponotangaTe tūpono o tētahi putanga, mai i te 0 ki te 1, mai i te 0% ki te 100% rānei. Tau kotahi: 1/37 = 2.70%.Pānuitia katoatia → o te hurihanga kotahi, koia i taea ai te tātari i te kēmu katoa ki runga i tētahi tauera pepa.
Ngā hurihanga maha
He motuhake ngā hurihanga, nō reira ka whakareatia ngā tūponotanga o tētahi raupapa. E rua ngā wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia → i muri tonu i a rāua: (18/37)² = 23.7%. He whero, kātahi ko te korewīraKoreTe kōhao kākāriki kotahi kāore e kapia e tētahi peti utu ōrite, tatini, tīwae rānei; te pūtake o te painga o te whare. Arā anō: kore kotahi, 0.Pānuitia katoatia →: (18/37)(1/37) = 1.3%. Ko te tekau mā whitu e rua ngā wā i muri tonu i a rāua: (1/37)² = 0.073%, tata ki te kotahi i roto i te 1,369. He mea nui te raupapa mō tētahi raupapa motuhake, engari ehara mō te tatau: ko “he whero, kātahi he pangopetiPangoHe peti utu ōrite ki ngā tau pango e 18. Wīwī: noir.Pānuitia katoatia →” he 25.0%, engari ko “kotahi te whero, kotahi te pango i ngā hurihanga e rua, ahakoa te raupapa” he 50.0%.
Kotahi te wā, nui ake rānei
Whakamahia te tauutuutu. Ko te tūpono kia kaua e puta he tau kotahipetiTau kotahiHe tau kotahi, ko te utunga 35:1.Pānuitia katoatia → i ngā hurihanga 37 he (36/37)³⁷ = 36.3%, nō reira ko te tūpono kia puta kotahi te wā neke atu he 63.7%, ehara i te “tino pono” e tūmanakohia ana e te maha o ngā kaitākaro i ngā tūpono 37 o te 1 i roto i te 37. E ai ki taua tātaitanga anō, tata ki te 1 i roto i te 3 te tūpono kia kore rawa tētahi tau e puta i ngā hurihanga 37, koia ka kitea i ia wā ētahi tau “makariri” i te papa hua.
Te wā tatari tūmanako
I te toharite ka puta tētahi tau kotahi kotahi te wā i ia hurihanga 37, engari he tino rerekē te roa o te tatari: ko te tau waenga o te tatari tata ki ngā hurihanga 25 (i te haurua o ngā wā ka tere ake tana puta), ā, kotahi i roto i ia rua tekau ngā tatari ka neke atu i ngā hurihanga 110. He roa te hiku o ngā wā tatari o tētahi tukanga āhuahanga, ā, ko te kaitākaro e “mōhio” ana kua tae te wā o tētahi tau i muri i ngā hurihanga 60, e whakaahua ana ia i tētahi mea ka puta kotahi i roto i ngā wā e rima.
Ngā hapa auau
Te tāpiri i ngā tūponotanga o ngā takahanga ka taea te puta tahi (ko te whero, ko te kehe rānei ehara i te 36/37; he 26/37, nā te mea tekau ngā tau he whero, he kehe hoki). Te whakarea mō ngā takahanga i te hurihanga kotahi (ko te whero me te kehe i te hurihanga kotahi he 10/37, ehara i te 18/37 × 18/37). Te whakaaro he wāhanga ngā hurihanga o mua o te raupapa e petihia ana e koe ināianei: i muri i ngā whero tekau, ko te tūpono o te whero tekau mā tahi he 18/37, ehara i te (18/37)¹¹.
He aha ngā tūpono i te rūreti, ā, he aha te rerekētanga ki te tūponotanga?
Ka whakahua ngā whare petipeti i ngā utungamoniUtungaTe moni ka whakahokia e te peti toa, ka kīia ko “X ki te 1”, hei tāpiri ki te moni peti ka whakahokia.Pānuitia katoatia → hei tūpono. Ka toa te tau kotahi i te tūponotanga 1/37, nō reira ko ngā tūpono ki te toa i te rūreti i te tau kotahi he 36 ki te 1 ki te whakahē. Nō reira ko te utunga 35 ki te 1 he waemoniWaeTe moni peti taketake e mahi ai tētahi pūnaha, tētahi kaitākaro rānei. Ka whakaahuatia ngā kauneke ki ngā wae kia hāngai ai ki ia tēpu.Pānuitia katoatia → kotahi te poto, ā, koinā te painga o te wharepāngarauPainga o te whareTe wāhanga o ia moni peti ka puritia e te whare petipeti i te toharite: 2.70% i te rūreti Ūropi.Pānuitia katoatia → i tōna āhua taketake. Te huri: tūpono whakahē = (1 − p)/p; tūponotanga = 1/(tūpono + 1).
Tātai
Ngā pātai
(1/37)² = 1/1369 ≈ 0.073%.
36/37 = 97.3%. Ko te kore te toenga.
He 1/37 ia tau o ngā tau 37. Ko te tekau mā whitu te tau e nui rawa ana te petihia, ā, he kōrero tērā mō te tangata.
He Pārekareka te Pāngarau
Me whakamātau koe i ēnei i te tuatahi. Kua kōpakina ia otinga; whakatuwherahia ina rite koe.
Ka peti koe ki te wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia →, i ia hurihanga, i ia hurihanga. He aha te tūpono ka puta tō toa tuarima i te hurihanga tuawaru tonu? Ā, e rima ō toa i roto i ngā hurihanga tuatahi e waru?
Whakaaturia te otinga
Whakautu 12.9%, tata ki te 1 i ngā 8, mō te toa tuarima i te hurihanga tuawaru. 33.4% mō ngā toa e rima i taua wā.
E rua ngā tikanga o te toa tuarima i te hurihanga tuawaru: ka toa te hurihanga tuawaru, ā, kei ngā hurihanga tuatahi e whitu ngā toa e whā tonu me ngā hinga e toru, ahakoa te raupapa. E 35 ngā ara hei whakatakoto i ngā toa e whā i waenga i ngā hurihanga e whitu.
Nō reira ko te tūpono ko 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9%.
Mō ngā toa e rima i te hurihanga tuawaru, tāpirihia te momo kīanga ōrite mō te toa tuarima i ngā hurihanga tuarima, tuaono me te tuawhitu: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%. Ka kīia tēnei e ngā kaitatauranga ko te tohatoha huarua tōraro: e hia ngā whakamātau e hiahiatia ana mō tētahi maha pūmau o ngā angitū. Ka mahia e Taylor (2021) taua pātai anō i te wīra Amerika, 12.2%.
He katakata iti
Tataua ngā kōhao. Wehea ki te 37. Whakareatia mō ngā raupapa. Kua oti.
Ngā Puna
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.