Njira yosavuta yothetsera mavuto a mwayi
Nkhani ya kuthekera ndi nkhani ya masamu yomwe imakumana nayo kawirikawiri m'masukulu chifukwa cha kuyandikira kwake kwa moyo watsiku ndi tsiku: kuyambira kuthekera kwa nambala kuwonekera pa dayisi, mpaka kujambula mpira wamitundu kuchokera m'bokosi, mpaka kuthekera kwa chochitika kuchitika kutengera deta. Tsoka ilo, ophunzira ambiri amaona kuti kuthekera ndi "kovuta" chifukwa mavutowo amawoneka osavuta, koma mayankho akhoza kukhala olakwika ngati sanaganiziridwe bwino. Komabe, pali njira yosavuta komanso yolongosoka yothetsera mavuto a kuthekera: kumvetsetsa mfundo zoyambira, kuzindikira mtundu wa vuto, kenako kusankha njira yoyenera.
Nkhaniyi ifotokoza njira zothandiza zomwe zingakuthandizeni kukhala achangu komanso olondola kwambiri pogwira ntchito pa mavuto a kuthekera.
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1. Kumvetsetsa lingaliro loyambira la mwayi
Kawirikawiri, mwayi wa chochitika \(A\) umalembedwa:
\[
P(A) = \frac{\text{number of outcomeths that support }A}{\text{number of all potentible outcometh}}
\]
Chinsinsi chili m'zinthu ziwiri:
1. Chitsanzo cha malo (S): zotsatira zonse zomwe zingachitike.
2. Chochitika (A): gawo la malo oyesera omwe akugwirizana ndi funso lofunsidwa.
Ngati zotsatira zonse zili zofanana (monga dayisi wolungama, ndalama zolungama), ndiye kuti njira yomwe ili pamwambapa ingagwiritsidwe ntchito mwachindunji. Ngati sizili zofanana, mwayi nthawi zambiri umawerengedwa kuchokera ku mitundu ina (monga deta ya pafupipafupi kapena kuthekera kokhazikika).
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2. Njira zachangu zothetsera mavuto a mwayi
Kuti musasocheretsedwe, gwiritsani ntchito "njira yogwirira ntchito" iyi:
1. Lembani zomwe zafunsidwa (chochitika chiti chomwe chapemphedwa?)
2. Dziwani malo a chitsanzo (pali zotsatira zingati zomwe zingatheke?)
3. Werengani zotsatira zomwe zikugwirizana ndi chochitika chomwe chapemphedwa.
4. Kugawana phindu kumathandizira zotsatira zonse
5. Chepetsani kachigawo ndipo onetsetsani kuti ndi koyenera (mwayi uyenera kukhala pakati pa 0 ndi 1)
Zolakwika zambiri zimachitika chifukwa chakuti magawo 2 ndi 3 sakufotokozedwa bwino.
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3. Gwiritsani ntchito matebulo, zithunzi za mitengo, kapena mndandanda ngati pakufunika kutero.
Pa mavuto okhudzana ndi mayesero awiri kapena kuposerapo (monga kutembenuza ndalama kawiri, kujambula khadi kawiri), njira zowonera zimathandiza kwambiri.
a) Tebulo
Yoyenera mitundu iwiri yosavuta, mwachitsanzo ndalama ndi dayisi.
b) Chithunzi cha mtengo
Yoyenera kuyesa pang'onopang'ono, makamaka ngati pali vuto la "kusabwerera" (chiwerengero cha zinthu chimasintha).
c) Mndandanda wa zitsanzo za malo
Yoyenera malo ang'onoang'ono oyezera zitsanzo.
Mwanjira iyi, simuyenera kuganiza.
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4. Mafunso achikhalidwe otheka ndi mayankho achangu
A. Mwayi pa dayisi
Ma dayisi ali ndi mbali 6: \(\{1,2,3,4,5,6\}\)
Chitsanzo: mwayi wopeza nambala yofanana.
– Malo oyesera \(S = 6\)
– Chochitika \(A = \{2,4,6\}\) ndi 3
– \(P(A) = 3/6 = 1/2\)
Njira yofulumira: nthawi zonse werengani "kuchuluka kwa zomwe zadzaza" m'malo mwa "zonse 6".
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B. Mwayi pa ndalama
Ndalama ili ndi mbali ziwiri: Mitu (A) ndi Mitu (G).
Chitsanzo: mwayi wopeza chithunzi pamene ndalama ikuponyedwa kamodzi kokha.
– Zonse 2
– Thandizo 1
– Mwayi \(=1/2\)
Ngati waponyedwa kawiri:
– Malo owerengera: \(\{AA, AG, GA, GG\}\) onse 4
Langizo lachidule: pa mayeso odziyimira pawokha, mwayi wonse nthawi zambiri umakhala \(2^n\) (wa ndalama) ndi \(6^n\) (wa dayisi).
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C. Kuthekera kotenga mpira kuchokera m'bokosi (ndi wolowa m'malo komanso wopanda wolowa m'malo)
Mwachitsanzo, bokosi lili ndi mipira itatu yofiira ndi mipira iwiri yabuluu (yonse 5).
1) Ndi kubweza
Tengani kawiri, nthawi iliyonse mpira ukabwezedwa. Mwayi woti mutenge wofiira kenako wabuluu:
– Mwayi wa kufiira: \(3/5\)
– Kenako buluu (chifukwa idabwezedwa, imatsala): \(2/5\)
– \(P = (3/5)(2/5)=6/25\)
2) Palibe kubweza
Tengani kawiri osabwerera. Mwayi woti mukhale wofiira kuposa wabuluu:
– Mwayi woyamba wofiira: \(3/5\)
– Mipira 4 yotsala, buluu yotsalayo imatsala 2 → mwayi wachiwiri wabuluu: \(2/4\)
– \(P = (3/5)(2/4)=6/20=3/10\)
Kusiyana kwakukulu: popanda kusinthidwa, chigawocho chimasintha chifukwa chiwerengero chonse cha mipira chimachepa.
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5. Gwiritsani ntchito malamulo owonjezera ndi owonjezera
A. Lamulo lowonjezera (OR)
Ngati mwafunsidwa mwayi wa "A kapena B", gwiritsani ntchito:
\[
P(A \chikho B) = P(A) + P(B) – P(A \chikho B)
\]
– \(A \cup B\): A kapena B (kapena zonse ziwiri)
– \(A \cap B\): A ndi B nthawi imodzi
Chitsanzo chosavuta: dayisi, mwayi wopeza nambala yofanana kapena kuchulukitsa kwa 3.
– Chofanana: {2,4,6} → 3
– Kuchulukitsa kwa 3: {3,6} → 2
– Zidutswa (zofanana ndi zochulukitsa za 3): {6} → 1
– Peluang: \((3/6)+(2/6)-(1/6)=4/6=2/3\)
B. Chowonjezera (chotsutsana)
Nthawi zambiri zimakhala zosavuta kuwerenga mawu akuti “sizinachitike” kenako nkuchotsa pa 1.
\[
P(A) = 1 – P(A^c)
\]
Chitsanzo: kuthekera kwa "mitu" kuwonekera kamodzi kokha pamene ndalama yaponyedwa katatu.
M'malo mowerengera nthawi 1, 2, 3 pa nambala, werengani chowonjezera chake:
– Zowonjezera: palibe manambala konse = manambala onse (GGG)
– \(P(\text{GGG}) = (1/2)^3 = 1/8\)
– Kotero \(P(\text{minimum 1 number}) = 1 – 1/8 = 7/8\)
Chinyengo ichi ndi chodziwika kwambiri pa mafunso "osachepera limodzi", "osachepera limodzi", "osachepera".
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6. Zovuta zokhudzana ndi malamulo: samalani ndi zina zowonjezera
Kuthekera kokhazikika kumatanthauza kuthekera kwa A kuchitika bola ngati B yachitika kale:
\[
P(A|B)=\frac{P(A \cap B)}{P(B)}
\]
Funso lamtunduwu nthawi zambiri limawonekera pakakhala zambiri zowonjezera, mwachitsanzo "zikudziwika kuti mpira wofiira unajambulidwa" kapena "zikudziwika kuti wophunzira wosankhidwayo anali mtsikana".
Njira yosavuta:
1. Yang'anani pa mkhalidwe B (ganizirani kuti malo a chitsanzo achepa kufika pa B yokha)
2. Kuchokera pa omwe akumana ndi B, werengani omwe akumananso ndi A.
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7. Zolakwika zofala kwambiri
1. Mwayiwala kusintha malo a chitsanzo popanda kusintha.
2. Kutanthauzira molakwika mawu akuti “kapena” (nthawi zina amatanthauza zonse ziwiri).
3. Kusalankhula momveka bwino ndi mawu akuti “osachepera” / “ambiri”; ndi bwino kugwiritsa ntchito mawu owonjezera.
4. Kuganiza kuti zochitika zili zodziyimira pawokha pomwe sizili (popanda kubwerera sizili zodziyimira pawokha).
5. Musamachepetse ndipo musayang'ane mfundo (zotsatira za kuthekera siziyenera kukhala >1).
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8. Yesetsani malangizo kuti mukhale waluso mwachangu
– Zolowerani kulemba: \(S\), \(A\), mamembala ambiri \(n(S)\), \(n(A)\).
- Yesetsani mavuto a "magawo awiri" pogwiritsa ntchito zithunzi za mitengo.
- Yesetsani mafunso "osachepera limodzi" okhala ndi mawu owonjezera.
– Mukapeza yankho, onani: kodi n’zomveka? Ngati mwayi wa chochitika “ungachitike,” mtengo wake nthawi zambiri umakhala pafupi ndi 1, osati pafupi ndi 0.
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Kutseka
Kuthetsa mavuto a kuthekera kumakhala kosavuta ngati mugwiritsa ntchito njira zokhazikika: fotokozani malo oyesera, dziwani zochitika, kenako werengerani chiŵerengero. Pamavuto ovuta kwambiri, gwiritsani ntchito zothandizira zowoneka monga matebulo kapena zithunzi za mitengo, ndikugwiritsa ntchito malamulo owonjezera, kuchulukitsa, ndi kuwonjezera. Mukachita mokwanira komanso kuwerenga mosamala mavuto, kuthekera sikudzamvekanso "chinyengo" koma m'malo mwake kudzakhala gawo la masamu omwe ndi osangalatsa chifukwa ali pafupi ndi zochitika za tsiku ndi tsiku.
Ngati mukufuna, ndithanso kupanga zitsanzo 10 za mafunso okhudzana ndi kuthekera pamodzi ndi mafotokozedwe awo (kuchokera pa zosavuta mpaka zovuta) kuti muthe kuchitapo kanthu nthawi yomweyo.
