Cov hauj lwm ntawm cov kev tshawb xav ntawm ntau yam nrog rau cov kev txiav txim siab. Muaj tseeb ziag rau Dummies

Mathematics Hoob no npaj cov menyuam kawm ntawv cov ib tug ntau ntawm surprises, yog ib tus uas - yog cov hauj lwm ntawm lub hom phiaj ntawm qhov muaj tseeb. Nrog rau cov kev txiav txim siab ntawm neeg ua num cov menyuam kawm ntawv muaj ib qho teeb meem nyob rau hauv yuav luag ib puas feem pua ntawm lub sij hawm. Yuav kom to taub thiab to taub lo lus nug no, koj yuav tsum paub cov kev cai, axioms, txhais cov ntsiab lus. Yuav kom to taub cov ntawv nyeem nyob rau hauv cov phau ntawv, koj yuav tsum paub tag nrho cov kev txiav nyiaj. Tag nrho cov no peb qhia rau koj kawm.

Science thiab nws daim ntawv thov

Txij li thaum peb muaj ib tug kev sib tsoo cov hoob kawm "Theory ntawm yuav tshwm rau Dummies", koj yuav tsum xub nkag rau hauv lub tswv yim thiab tsab ntawv abbreviations. Yuav pib txhais tau cov notion "probability kev tshawb xav". Yuav ua li cas hom ntawm science yog thiab zoo li cas yog nws rau? Muaj tseeb kev tshawb xav - nws yog ib tug ntawm cov ceg ntawm kev kawm txog zauv uas kawm cov phenomena thiab random qhov tseem ceeb. Nws kuj tshuaj xyuas cov qauv, lub zog thiab ua hauj lwm tau nrog cov random zog. Yog vim li cas yog nws tsim nyog? Thoob plaws science yog nyob rau hauv txoj kev tshawb no ntawm tej yam ntuj tso phenomena. Tej yam ntuj tso thiab lub cev dab ua tsis tau tsis muaj cov randomness. Txawm hais tias thaum lub sij hawm xyaum ua tej yam raug kaw raws li meej li sai tau qhov kev tshwm sim, yog tias pheej rov qab ua tib xeem nrog ib tug high school cov probability cov tshwm sim yuav tsis tau tib yam.

Piv txwv ntawm cov teeb meem nyob rau hauv ntau yam kev tshawb xav peb yuav xav txog hais tias koj yuav saib koj tus kheej. Lub sij hawm nyob ntawm muaj ntau ntau yam tseem ceeb, uas yog zoo tsis yooj yim sua mus rau hauv tus account los yog sau npe, tab sis lawv muaj ib tug tej yam loj loj nyob rau hauv lub sij hawm ntawm qhov xyaum ua tej. Cuab piv txwv yog qhov teeb meem ntawm kev txiav txim trajectory ntawm lub ntiaj teb los yog qhov kev txiav txim ntawm cov huab cua forecast, qhov tshwm sim rau encountering ib acquaintance rau txoj kev mus ua hauj lwm thiab kev txiav txim ntawm lub qhov siab ntawm lub dhia ua kis las. Nws tseem yog lub hom phiaj ntawm qhov muaj tseeb yog ntawm kuj zoo kawg kev pab rau cov brokers rau Tshuag exchanges. Cov hauj lwm ntawm cov kev tshawb xav ntawm ntau yam, qhov kev txiav txim ntawm cov uas yav tas los muaj ntau yam teeb meem yuav ua tau rau koj ib tug tiag tiag trifle tom qab peb los yog plaub piv txwv hauv qab no.

txheej xwm

Raws li hais ua ntej lawm, science yog kawm cov txheej xwm. Muaj tseeb kev tshawb xav, piv txwv ntawm kev daws teeb meem, peb yuav xav txog rau yav tom ntej, kev kawm tsuas yog ib hom - random. Cuaj kaum, koj yuav tsum paub tias tej yam uas yuav ua tau ntawm peb yam:

• Tsis yooj yim sua.
• Txhim khu kev qha.
• Random.

Peb muab me ntsis stipulate txhua ntawm lawv. Tsis yooj yim sua tshwm sim yuav tsis tshwm sim nyob rau hauv txhua yam. Piv txwv yog: lub khov ntawm cov dej rau ib kub saum toj no zero Extruding lub voos xwmfab lub hnab ntawm cov khoom.

Tej yam kev tshwm sim yeej ib txwm yuav siv sij hawm qhov chaw nrog tsis paub tseeb, yog tias tag nrho cov tej yam kev mob. Piv txwv li, koj tau txais nyiaj ua hauj lwm rau lawv ua hauj lwm, tau txais ib daim ntawv kawm tiav qib siab kev kawm ntawv, yog tias rau siab ntso ua kawm, dhau lub xeem thiab tiv thaiv lawv daim diploma thiab thiaj li nyob.

Nrog random txheej xwm ib tug me ntsis ntau tham: nyob rau hauv lub chav kawm ntawm qhov xyaum ua tej, nws yuav tshwm sim los yog tsis, piv txwv li, rub ib tug ace los ntawm daim ntawv lawj, ua ib tug tshaj plaws ntawm peb cov me nyuam. Cov yuav tau raws li nrog rau cov thawj los, thiab yog li ntawd, nyob rau hauv Feem ntau, tsis tau. Nws yog tej zaum cov keeb kwm ntawm cov kev tshwm sim thiab yog kawm science.

probability

Nws yog feem ntau ntsuam xyuas tau ib tug muaj kev vam meej lub sij hawm ntawm kev, nyob rau hauv uas cov kev tshwm sim no tshwm sim. Qhov ntau yog kwv yees li ntawm ib tug zoo qib, tshwj xeeb tshaj yog yog hais ntau kev ntsuam xyuas yog tsis yooj yim sua los yog tsis yooj yim. Cov hauj lwm ntawm cov kev tshawb xav ntawm ntau yam nrog rau cov kev txiav txim siab, los yog es nrog qhov kev soj ntsuam ntawm ntau yam ntawm ib tug kev tshwm sim, txhais tau tias nrhiav tus heev tau qhia tawm ntawm ib tug muaj kev vam meej lub sij hawm. Muaj tseeb nyob rau hauv kev kawm txog zauv - ib tug hais txog zauv cov yam ntxwv ntawm cov kev tshwm sim. Nws yuav siv sij hawm qhov tseem ceeb ntawm xoom mus rau ib, denoted los ntawm tsab ntawv P. Yog hais tias P sib npaug pes tsawg, cov kev tshwm sim muaj peev xwm tsis tshwm sim yog hais tias tus unit, cov kev tshwm sim yuav muab qhov chaw nrog tsis muaj tseeb. Qhov ntau P txuas sib sau, cov muaj muaj zog yuav ua rau muaj ib tug muaj kev vam meej lub sij hawm, thiab vice versa, yog hais tias nws yog nyob ze rau zero, thiab cov kev tshwm sim yuav tshwm sim nrog ib tug tsawg yuav qhov muaj tseeb.

abbreviations

Cov hauj lwm ntawm cov kev tshawb xav ntawm ntau yam, nrog rau cov kev txiav txim siab uas koj yuav pom me ntsis sai, tej zaum yuav muaj cov nram qab no abbreviations:

• !;
• {};
• N;
• P thiab P (X);
• A, B, C, thiab lwm yam .;
• n;
• m.

Muaj ib co neeg: ntxiv piav yuav tsum ua raws li tsim nyog. Peb qhia rau pib nrog, piav qhia txog cov yuav txo tau hais saum toj no. Thawj rau peb daim ntawv teev yog pom factorial. Nyob rau hauv thiaj li yuav ua kom nws ntshiab, peb muab piv txwv: 5 = 1 * 2 * 3 * 4 * 5 los yog 3 = 1 * 2 * 3 !. Ntxiv mus, nyob rau hauv kev zawm hniav sau predetermined plurality ntawm, piv txwv li {1; 2; 3; 4; ..; n} los yog {10; 140; 400; 562}. Cov nram qab no cim - ib tug txheej ntawm tej yam ntuj tso tus xov tooj yog heev nyob rau hauv tej hauj lwm uas yuav tshwm sim kev tshawb xav. Raws li tau teev ua ntej lawm, P - yog muaj tseeb, thiab P (X) - yog qhov yuav tshwm ntawm kev tshwm sim tshwm sim H. latin tsiaj ntawv denoted cov txheej xwm, rau Piv txwv li: A - ntes tau dawb pob B - xiav, C - liab los yog, feem ,. Me tsab ntawv n - yog tus naj npawb ntawm tag nrho cov tshwm sim tau, thiab m - tus naj npawb ntawm affluent. Li no, peb muab tau cov classical txoj cai rau kev nrhiav ib tug ntau yam ntawm elementary paub tab: F = m / n. Lub hom phiaj ntawm qhov muaj tseeb "rau Dummies", tej zaum, thiab tag rau cov kev txawj ntse. Tam sim no luag tus kev hloov rau cov tshuaj.

Txog cov teeb meem 1. combinatorics

Kawm Ntawv Pab Pawg ntiav peb caug cov neeg, cov uas koj yuav tsum xaiv cov laus, nws deputy thiab cov khw tub qhe. Koj yuav tau mus nrhiav ib tug xov tooj ntawm txoj kev ua li no kev txiav txim. Xws li ib tug hauj lwm yuav tshwm sim nyob rau hauv cov kev kuaj mob. Kev tshawb xav ntawm ntau yam, uas cov paub tab peb muaj tam sim no xav tias yuav, yuav muaj xws li kev pab raws qib los ntawm cov chav kawm ntawm combinatorics, yuav nrhiav ib tug classical, geometrical thiab cov hom phiaj rau qhov yooj yim mis. Nyob rau hauv qhov kev piv txwv, peb yuav daws tau qhov hauj lwm ntawm kev kawm combinatorics. Peb npaj mus rau ib tug txiav txim siab. Qhov no ua hauj lwm tsis yog yooj yim:

1. n1 = 30 - tau tswj cov tub ntxhais kawm ntawv pab pawg neeg;
2. n2 = 29 - cov neeg uas muaj peev xwm coj cov ncej ntawm deputy;
3. n3 = 28 neeg ua ntawv thov rau khw tub qhe.

Txhua yam peb tau ua yog nrhiav qhov zoo tshaj plaws ntawm cov kev xaiv, uas yog mus muab tag nrho cov nuj nqis. Raws li ib tug tshwm sim, peb tau txais: 30 * 29 * 28 = 24360.

Qhov no yuav tsum tau cov lus teb rau lo lus nug no.

Txog cov teeb meem 2. rearrange

Thaum lub rooj sib tham 6 koom, qhov kev txiav txim txiav txim los yog nqus ntau ntau. Peb yuav tsum nrhiav cov xov tooj uas tau xaiv rau lub kos. Nyob rau hauv qhov kev piv txwv, peb xav txog ib tug permutation ntawm rau hais, hais tias yog, peb yuav tau mus nrhiav ib tug 6!

Nqe txiav peb twb hais, nws yog dab tsi thiab yuav ua li cas xam. Tag nrho nws hloov tawm hais tias muaj 720 kev xaiv rau tus kos. Thaum xub thawj siab ib muag, tsis yooj yim ua hauj lwm yog heev luv luv thiab yooj yim tov. Qhov no yog qhov ua hauj lwm uas tshuaj xyuas qhov kev tshawb xav ntawm ntau yam. Yuav ua li cas los daws kom tau cov teeb meem ntawm ib tug ntau dua theem, peb yuav saib cov nram qab no piv txwv.

ua hauj lwm 3

Ib pab pawg neeg ntawm cov tub ntxhais kawm los ntawm nees nkaum-tsib cov txiv neej yuav tsum tau muab faib ua peb pawg neeg ntawm cov rau, cuaj thiab kaum. Peb muaj: n = 25, k = 3, n1 = 6, n2 = 9, n3 = 10. Nws tseem mus hloov qhov tseeb qhov tseem ceeb nyob rau hauv cov mis, peb tau txais: N25 (6,9,10). Tom qab tej yam yooj yim suav peb tau txais ib cov lus teb - 16,360,143 800. Muaj cov ncauj Yog hais tias txoj hauj lwm tsis hais tias nws yog tsim nyog los tau ib tug zauv tov, peb yuav muab nws nyob rau hauv daim ntawv ntawm cov factorials.

neeg ua hauj lwm 4

Peb cov neeg tsis paub hais tias xov tooj los ntawm ib tug mus rau kaum. Nrhiav qhov kwv yees tias ib tug neeg yuav phim tus xov tooj. Ua ntej peb yuav tsum paub lub xov tooj ntawm tag nrho cov hauj lwm tshwm sim - nyob rau hauv cov ntaub ntawv no, ib txhiab, uas yog, kaum nyob rau hauv lub thib peb degree. Tam sim no peb nrhiav tau lub xov tooj ntawm cov kev xaiv uas ua rau los muaj tseeb tag nrho cov txawv tus xov tooj uas muab mus rau kaum, cuaj thiab yim. Qhov twg puas tau cov zauv? Tus thawj xav tias ntawm tus xov tooj nws muaj kaum xaiv, lub thib ob yog cuaj, thiab lub thib peb yuav tsum tau xaiv los ntawm lub yim seem, thiaj tau 720 tau xaiv. Raws li peb twb pom tau hais tias saum toj no, tag nrho cov variants ntawm 1000, thiab 720 tsis muaj repetition, yog li ntawd, peb xav nyob rau hauv seem 280. Tam sim no peb xav tau ib tug formula rau nrhiav txoj kev classical probability: P =. Peb tau txais ib lo lus teb: 0,28.