Matematika ʻo e Lulēti · Palopalema matematika · miniti ʻe 7

Palopalema: ʻE Fēfē Hono Lōloa Kae Hū ʻa e Noa

ʻOku hū ʻa e noa ʻi he vilo ʻe taha ʻi he 37 ʻi he ʻavalisi. ʻE fēfē hono fuoloa moʻoni ʻo hoʻo tatali, pea ko e hā ʻoku ne fai ki ha tokotaha peti totongi tatau?

Tali nounou

Ko e tatali ki he noa ʻoku fakasioemetili: ʻavalisi ko e vilo ʻe 37, fika lotoloto ko e 25, pea ko e tatali ʻe taha ʻi he uofulu ʻoku lahi ange ʻi he vilo ʻe 110. ʻI ha taimi vaʻinga ʻo e vilo ʻe 200, ʻoku ʻamanekina ʻe ha tokotaha peti totongi tatau ha noa ʻe 5.4 pea te ne sio ki ha meʻa pē mei he 1 ki he 10.

tatali ʻavalisi
vilo ʻe 37
tatali lotoloto
vilo ʻe 25
p(ʻikai ha noa ʻi he vilo ʻe 100)
6.5%
ngaahi noa ʻi he vilo ʻe 200
5.4 ± 2.3

Ko e palopalema

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 → ʻo e 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 → ko e 1/37 ʻi he vilo. (a) Ko e hā ʻa e ngalingali ke ʻikai ha noa ʻi he vilo hoko ʻe 37? (b) Ko e hā ʻa e tatali lotoloto? (c) ʻI ha taimi vaʻinga totongi tatau ʻo e vilo ʻe 200, ko e noa ʻe fiha ʻoku totonu ke ʻamanekina ʻe ha tokotaha vaʻinga, pea ko e hā hono vahaʻa?

Ngaahi solovaʻanga

(a) (36/37)³⁷ = 36.3%. ʻI he lahi ange ʻi he vahe tolu ʻo e taimi, ʻoku ʻosi ha vilo ʻe 37 ʻo ʻikai ha noa ʻe taha, ʻa ia ko e fika tatau ia mo e “tau ʻo siʻi taha ʻi he tuʻo taha ʻi ha peti fika ʻe tahapetiPeti fika ʻe tahaFika pē ʻe taha, totongi ʻo e 35:1.Lau kotoa → ʻi he vilo ʻe 37” ʻoku 63.7% pē. (b) ʻOku fakasioemetili ʻa e tatali W; p(W > k) = (36/37)ᵏ; ko e fika lotoloto ko e k ʻoku kolosi ai ʻeni ʻa e 0.5, ʻa ia ko e k ≈ 25. Ko e vaeua ʻo e ngaahi tatali ko e vilo ʻe 25 pe nounou ange pea ko e vaeua ʻoku lōloa ange; ʻoku tohoʻi hake ʻa e ʻavalisi ʻo e 37 ʻe he hiku lōloa. (c) Ko e ngaahi noa ʻi he vilo ʻe 200 ʻoku painomiale mo e ʻavalisi ʻo e 200/37 = 5.4 mo e mavahe fakasitanatematematikaMavahe fakasitanateAka ua ʻo e vēliani; ko e mamaʻo angamaheni ʻo ha ola mei he mahuʻinga ʻamanekina.Lau kotoa → ʻo e √(200 × (1/37) × (36/37)) ≈ 2.3. Ko ha vahaʻa ʻo e 95% ʻoku meimei 1 ki he 10.

tatali ki he noangalingali
ʻi loto ʻi he vilo ʻe 1024.0%
ʻi loto ʻi he vilo ʻe 2549.6%
ʻi loto ʻi he vilo ʻe 3763.7%
ʻi loto ʻi he vilo ʻe 5074.6%
ʻi loto ʻi he vilo ʻe 10093.5%
lahi ange ʻi he vilo ʻe 110≈ 5%
lahi ange ʻi he vilo ʻe 2000.4%
p(W ≤ k) = 1 − (36/37)ᵏ. ʻAvalisi 37, fika lotoloto 25.

Ko e fakamole ʻo e noa ki ha tokotaha peti totongi tatau

ʻOku fakamole ʻe he noa taki taha ha peti ʻe taha, pea ko e ngaahi noa ko e tuʻunga lelei kotoa ia ʻi he kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa →: ʻi ha vilo ʻavalisi ʻe 37, ʻoku fefakaleluʻaki ʻa e ikuna ʻe 18 mo e mole ʻe 18, pea ko e noa ʻe taha ko e −1/37. ʻI ha taimi vaʻinga ʻo e vilo ʻe 200 ʻi he $10, ʻoku fakamole ʻe he noa ʻamanekina ʻe 5.4 ʻa e $54, ʻa ia ʻoku tatau tofu pē mo e 200 × $10 / 37. Ko ha taimi vaʻinga mo e noa ʻe 2 kuo maʻu ai ha monūʻia lelei ʻo e $34; ko ha taimi vaʻinga mo e noa ʻe 9 kuo maʻu ai ha monūʻia kovi ʻo e $36, pea ʻe ongo ia ʻo hangē kuo kākaaʻi. ʻI ha tēpile la partagelaoLa partageLao faka-Falanisē: ʻi he hū ʻa e noa, ʻoku fakafoki ʻa e vaeua ʻo ha peti totongi tatau. ʻOku vaeua ai ʻa e tuʻunga lelei ʻo e kasino ʻi he ngaahi peti ko ia ki he 1.35%.Lau kotoa →, ʻoku fakamole ʻe he noa taki taha ʻa e vaeua ʻo ha peti pea ʻoku vaeua ʻa e ngaahi fika.

Ngaahi noa ʻi ha taimi vaʻinga ʻo e vilo ʻe 200% ʻo e ngaahi taimi vaʻinga
0–1
2.5%
2–3
18%
4–5
34%
6–7
28%
8–9
13%
10 pe lahi ange
4.5%
% ʻo e ngaahi taimi vaʻinga
01734%
Painomiale(200, 1/37). ʻOku totongi ʻe he tokotaha peti kulokula $10 ʻa e $10 ki he noa taki taha; ko e movetevete ʻo e ngaahi noa ko e movetevete ia ʻo e totongi ʻo e efiafi.

Lao La Partage ʻi he LulētiʻOku Kākā ʻa e Lulēti ʻi he ʻInitaneti? Ko e Tui Hala

Ko e fehuʻi hoko

Ko e hā ʻa e ngalingali ʻo ha noa ʻe ua hokohoko? (1/37)² = 1/1,369. ʻI ha kasino ʻoku fakalele ai ha tēpile ʻe 20 ʻi he vilo ʻe 50 ʻi he houa, ʻoku meimei hoko ha noa ʻe ua hokohoko ʻi ha feituʻu ʻi he houa ʻe 1.4 kotoa pē. ʻOku pehē ʻe he kau vaʻinga ʻoku sio ki ai kuo maumau ʻa e veʻeteka; ka ʻoku pehē ʻe he fika ko ha ʻaho Tūsite angamaheni pē ia.

Sivi ia

ʻOku lau ʻe he Meʻa Faʻifaʻitaki ʻo ha Taimi Vaʻinga Lulēti ʻa e ngaahi noa ʻi he taimi vaʻinga taki taha. Fakalele ha vilo ʻe 100 ʻo tuʻo laungeau pea tā ʻa e lau: ʻe hā mai ʻa e histokalami ʻi ʻolunga, mo hono hiku lōloa ki he toʻomataʻu. Ko e hiku ko e feituʻu ia ʻoku haʻu mei ai ʻa e ngaahi talanoa.

Fomula

p(W > k) = (36/37)ᵏ
E[W] = 37 · fika lotoloto ≈ 25
ngaahi noa ʻi he vilo ʻe N ~ Painomiale(N, 1/37)

Ngaahi fehuʻi

ʻOku ngalingali lahi ange ʻa e noa ʻi ha ngaahi veʻeteka ʻe niʻihi?

ʻIkai ʻi ha veʻeteka faitotonu. ʻI ha veʻeteka hehemalēpiVeʻeteka hehemaKo ha veʻeteka ʻoku ʻi ai hano ngaahi maumau fakatuʻasino ʻoku ne ʻai ke ngalingali lahi ange ʻa e ngaahi luo ʻe niʻihi ʻi he 1/37. ʻOku tātāitaha, pea ʻoku ʻiloʻi pē ʻaki ha ngaahi afe ʻo e ngaahi vilo kuo hiki.Lau kotoa → ʻe lava ke pehē ha luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → pē, pea ʻe fiemaʻu ha vilo ʻe lauafe ke ʻiloʻi ai.

ʻOku totonu ke u tuku maʻu pē ha sipi ki he noa ko ha malu?

Ko ha peti ia ʻo e 2.70% ʻo hangē ko e toenga kotoa. ʻOku ne liliu ʻa e fōtunga ʻo e taimi vaʻinga (ʻoku hoko ʻa e noa ko ha ikuna) kae ʻikai ko e fakamole.

Ko e hā ʻoku siʻi ange ai ʻa e fika lotoloto ʻi he ʻavalisi?

Koeʻuhí ʻoku taʻefakatatau ʻa e tufaki ʻo e ngaahi tatali: lahi ʻa e ngaahi tatali nounou, mo ha niʻihi siʻi ʻoku lōloa ʻaupito.

Meʻa fakaoli

ʻAvalisi 37, fika lotoloto 25, mo ha hiku lōloa ʻoku nofo ai ʻa e ngaahi talatupuʻa.

ʻAvalisi 37, fika lotoloto 25, mo ha hiku lōloa ʻoku nofo ai ʻa e ngaahi talatupuʻa.

Ngaahi Maʻuʻanga

  1. 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.
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Vahe 13, lulēti.
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