Matematika ʻo e Lulēti · Palopalema matematika · miniti ʻe 7

Palopalema: Ko e Veʻeteka ʻAho Fāʻeleʻi

Ko e vilo ʻe fiha kimuʻa pea toe hā ha fika? Siʻi ange ʻaupito ia ʻi he fakafuofua ʻa e lahi taha ʻo e kakai.

Tali nounou

Ko e palopalema ʻo e ʻaho fāʻeleʻi ʻi ha veʻeteka ʻo e luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → ʻe 37: hili pē ha vilo ʻe 8, ʻoku lahi ange ʻi he vaeua ʻa e ngalingali kuo hā ha fika ʻo tuʻo ua. ʻOku lau ʻe he kau vaʻinga ʻa e ngaahi toe hā ko ha ngaahi sīpinga; ka ko e anga ʻamanekina pē ia ʻo ha veʻeteka faitotonu.

ngalingali 50% ki ha toe hā

vilo ʻe 8

ngalingali 90%

vilo ʻe 14

ngalingali 99%

vilo ʻe 20

ngaahi vilo ʻamanekina ki he ʻuluaki toe hā

≈ 8.3

Ko e palopalema

Vilo ha veʻeteka ʻIulope faitotonu. ʻE fiha ʻa e ngaahi vilo kae ʻoua kuo lahi ange ʻi he vaeua ʻa 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 → kuo hā ʻa e fika tatau ʻi ha vilo ʻe ua ʻo siʻi taha? ʻOku fakafuofua ʻe he lahi taha ʻo e kau vaʻinga ʻoku meimei 18 pe 19, ko e vaeua ʻo e 37. Ko e tali ko e 8.

Ko e solovaʻanga

Fakakaukauʻi ʻa e ngalingali ʻo e ʻikai ha toe hā pea toʻo ia mei he taha. Hili ha vilo ʻe k, p(kehekehe kotoa) = (37/37)(36/37)(35/37)…((38 − k)/37). Ki he k = 8: 1 × 0.973 × 0.946 × 0.919 × 0.892 × 0.865 × 0.838 × 0.811 ≈ 0.44, ko ia ko e p(ha toe hā) ≈ 0.56. Ki he k = 14 ko e 0.93; ki he k = 20 ko e 0.996. ʻOku tō ʻa e fakakaukau fakanatula koeʻuhí ʻoku tupu ʻa e lahi ʻo e ngaahi hoa vilo ʻo hangē ko e k², pea ʻe lava ke tatau ha hoa pē.

ngaahi vilo kp(kehekehe kotoa)p(toe hā ʻo siʻi taha ʻi he tuʻo taha)

575.7%24.3%

843.8%56.2%

1026.4%73.6%

147.1%92.9%

200.4%99.6%

37≈ 0%≈ 100%

p(ʻikai ha toe hā) = 37! / ((37 − k)! · 37ᵏ).

Ko e ʻuhinga ʻoku mahuʻinga ai ʻi he tēpile

ʻE meimei fakahā maʻu pē ʻe ha papa ola ʻo e fika fakamuimui ʻe 20 ha toe hā ʻe taha ʻo siʻi taha, ʻo faʻa ua pe tolu. ʻOku sio ʻa e kau vaʻinga ki he “naʻe hā ʻa e 17 ʻo tuʻo ua ʻi he vilo ʻe hongofulu” pea nau pehē ko e 17 ko ha fika vela; ka ʻoku pehē ʻe he fika ʻo e ʻaho fāʻeleʻi ʻoku hoko ha toe hā ʻi loto ʻi he vilo ʻe hongofulu ʻi he 74% ʻo e taimi pea ko e fika ʻoku toe hā ʻoku taʻefakataumuʻa. ʻOku moʻoni ʻa e sīpinga; ka ʻoku ʻikai moʻoni hono ʻuhinga.

Ngalingali kuo toe hā ha fika hili ha vilo ʻe k%

vilo ʻe 4

16%

vilo ʻe 6

36%

vilo ʻe 8

56%

vilo ʻe 10

74%

vilo ʻe 14

93%

vilo ʻe 20

99.6%

049.8099.6%

Ngaahi Ola ʻo e Lulēti: Lau ʻo e Papa

Ko e palopalema hoko

ʻE fiha ʻa e ngaahi vilo kae ʻoua kuo hā ʻo tuʻo ua ha fika pau, hangē ko e 17? Ko ha fehuʻi kehe ia mo ha tali lahi ange ʻaupito: ko e tatali ʻamanekina ko e vilo ʻe 74, pea ko e ngalingali ʻo e 17 ʻe ua ʻi loto ʻi he vilo ʻe 20 ko e meimei 10%. Ko e kehekehe ʻi he vahaʻa ʻo e “toe hā ha fika” (vilo ʻe 8) mo e “toe hā ʻa e fika ni” (vilo ʻe 74) ko e kehekehe kotoa ia ʻi he vahaʻa ʻo ha sīpinga ʻoku ke tokanga ki ai ʻi he hili ia mo ha tala ʻoku ke fai kimuʻa.

Sivi ia

Fakalele ʻa e Vaʻinga Fakatātā ʻi ha vilo ʻe hongofulu pea sio ki he hisitōlia. ʻE faʻa ʻi ai ha toe hā. Toe fakalele ia. ʻE kehe ʻa e fika ʻoku toe hā. Fai ʻeni ʻo tuʻo hongofulu pea kuo ke sio ki he palopalema ʻo e ʻaho fāʻeleʻimatematikaPalopalema ʻo e ʻaho fāʻeleʻiKo e tokolahi ʻo e kakai ʻoku fiemaʻu kimuʻa pea ngalingali ke tatau ʻa e ʻaho fāʻeleʻi ʻo ha toko ua, pe ko e lahi ʻo e ngaahi vilo kimuʻa pea ngalingali ke toe hū ha fika. ʻI ha veʻeteka luo ʻe 37, ʻoku feʻunga ʻa e vilo ʻe 8 ki ha faingamālie ʻoku lahi ange ʻi he vaeua.Lau kotoa →; fai ia ʻo tuʻo afe (ʻe lava ʻe he ngaahi meʻa faʻifaʻitaki) pea kuo ke fuaʻi ia.

Fomula

p(ʻikai ha toe hā ʻi he k) = Π (38 − i)/37 ki he i = 1…k

p(toe hā) = 1 − p(ʻikai ha toe hā)

Ngaahi fehuʻi

ʻOku tatau ʻeni mo e palatoki ʻo e ʻaho fāʻeleʻi?

Tatau tofu pē, mo e luo ʻe 37 ʻo ʻikai ko e ʻaho ʻe 365. ʻOku ʻomi ʻe he kakai ʻe toko 23 ʻa e 50% ki he ngaahi ʻaho fāʻeleʻi; ʻoku ʻomi ʻe he vilo ʻe 8 ʻa e 56% ki he veʻeteka.

Fēfē ʻa e fika tatau ʻe tolu?

50% hili ha meimei vilo ʻe 19. ʻOku kei angamaheni pē.

ʻOku fakahā ʻe ha toe hā ha hehema?

ʻIkai. ʻE fakahā ia ʻe ha vilo ʻe lauafe mei ha veʻeteka ʻe taha; ka ʻoku ʻikai ʻaupito fakahā ia ʻe ha toe hā.

Vaʻinga mo e Matematika

ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.

ʻOku fakahā ʻe ha papa ola ʻi he tafaʻaki ʻo ha veʻeteka ʻAmelika ʻa e vilo fakamuimui ʻe 16. ʻOku fēfē ʻa e ngalingali ke ʻoua naʻa hā tuʻo ua ha fika ʻi ai?
Fakahā ʻa e tali
Tali Meimei 2.5%: ʻoku fakahā ʻe he meimei papa ʻe 39 ʻi he 40 ha fika ʻoku toe hā mai ʻo taha pe lahi ange.
Fai ʻo vilo ki he vilo. ʻE lava ke hoko ʻa e ʻuluaki vilo ko ha fika pē. Ko hono ua kuo pau ke ʻoua naʻa tatau mo ia: faingamālie ʻe 37 ʻi he 38. Ko hono tolu kuo pau ke ʻoua naʻa tatau mo e ongo fika: 36 ʻi he 38. Ko hono hongofulu mā ono kuo pau ke ʻoua naʻa tatau mo ha fika ʻe hongofulu mā nima: 23 ʻi he 38.
Liunga: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0.0246.
Ko ha papa ʻoku ʻikai ha fika toe hā ko e meʻa tātātaha ia. Ko ha papa ʻoku ʻi ai ha fika toe hā ʻoku ʻikai ha meʻa ʻoku ne fakahā fekauʻaki mo e veʻeteka.
ʻI he vilo ʻe hongofulu ʻo ha veʻeteka ʻIulope, ko e hā ʻa e ngalingali ke hū mai ʻa e 17 ʻo liunga nima tofu pē? Ke hū mai ha fika, ha fika pē, ʻo liunga nima pe lahi ange? Pea ke hū mai ha fika ʻo liunga tolu ʻi he siʻi taha ʻi he vilo ʻe fā?
Fakahā ʻa e tali
Tali 17 ʻo liunga nima tofu pē: 1 ʻi he 315,576. Ha fika ʻo liunga nima pe lahi ange: meimei 1 ʻi he 8,333. Ha fika ʻo liunga tolu pe lahi ange ʻi he vilo ʻe fā: 1 ʻi he 349.
17 ʻo liunga nima: fili pe ko e fē nima ʻo e vilo ʻe hongofulu, founga ʻe 252, ʻoku taki taha hono ngalingali ʻo e (1/37)⁵ × (36/37)⁵. Fakataha, 1 ʻi he 315,576.
Ha fika pē: ʻoku taki taha ʻa e fika ʻe 37 mo hono ngalingali ʻo e 1 ʻi he 308,325 ke tau ʻo liunga nima pe lahi ange, ʻa ia ʻoku ʻomai ai ʻa e 37 ʻi he 308,325, pe 1 ʻi he 8,333. Ko e meʻa tātātaha ʻo ha fika ʻe ua ʻoku tau taki taha ʻo liunga nima ʻoku lau tuʻo ua, ka ko hono toʻo ʻoku ʻikai liliu ai ha meʻa ʻi he tuʻunga totonu ko ʻeni.
Liunga tolu ʻi he vilo ʻe fā: ki ha fika ʻe taha, 4 × 36 + 1 = 145 ʻo e ola ʻe 37⁴ ʻe ala hoko; ki ha taha pē ʻo e fika ʻe 37, 145/37³ = 1 ʻi he 349.
Ki ha veʻeteka noaveʻetekaNoaKo e luo lanu mata pē ʻe taha ʻoku ʻikai kāpui ʻe ha peti totongi tatau, peti tasini pe peti kōlomu; ko e tupuʻanga ia ʻo e tuʻunga lelei ʻo e kasino. ʻOku toe ui: noa ʻe taha, 0.Lau kotoa → ua, ko e ngaahi fika tatau ko e 1 ʻi he 359,275, 1 ʻi he 9,243 mo e 1 ʻi he 368. Ko e vaha ʻi he vahaʻa ʻo e “17” mo e “ha fika pē” ko e palopalema ʻo e ʻaho fāʻeleʻimatematikaPalopalema ʻo e ʻaho fāʻeleʻiKo e tokolahi ʻo e kakai ʻoku fiemaʻu kimuʻa pea ngalingali ke tatau ʻa e ʻaho fāʻeleʻi ʻo ha toko ua, pe ko e lahi ʻo e ngaahi vilo kimuʻa pea ngalingali ke toe hū ha fika. ʻI ha veʻeteka luo ʻe 37, ʻoku feʻunga ʻa e vilo ʻe 8 ki ha faingamālie ʻoku lahi ange ʻi he vaeua.Lau kotoa → ia ʻo toe: ʻoku ʻi ai ʻa e founga ʻe 37 ke ke ofo ai.

Meʻa fakaoli

$ʻOku vave ʻa e toe hā ʻa e meʻa ʻe taha. Ko e meʻa ko iá ʻoku taʻefakataumuʻa.$

ʻOku vave ʻa e toe hā ʻa e meʻa ʻe taha. Ko e meʻa ko iá ʻoku taʻefakataumuʻa.

Ngaahi Maʻuʻanga

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, paaki hono 3, 1968. Ko e ʻosi ʻa e paʻanga ʻa e tokotaha peti, vahe XIV.
Wizard of Odds. “Ask the Wizard”, roulette questions. Fakafoʻou ʻAokosi 3, 2026.

naʻe vakaiʻi 2026-09-28mōtolo: ʻIulope, noa ʻe tahafounga ngāue ↗ngaahi maʻuʻanga ↗