Ntau zaus hauv lub neej peb tau ntsib nrog qhov xav tau los ntsuas qhov muaj feem yuav tshwm sim. Txawm hais tias nws tsim nyog yuav daim pib rho npe lossis tsis, yuav ua li cas yog poj niam txiv neej ntawm tus menyuam thib peb hauv tsev neeg, txawm tias huab cua yuav ntshiab tag kis lossis nws yuav los nag dua - muaj cov piv txwv zoo li no suav tsis txheeb. Hauv qhov yooj yim tshaj plaws, koj yuav tsum faib cov naj npawb ntawm cov txiaj ntsig zoo los ntawm tag nrho cov xwm txheej. Yog tias muaj 10 daim pib sib tw hauv kev rho npe, thiab muaj 50 tag nrho, ces txoj hauv kev tau txais txiaj ntsig yog 10/50=0.2, uas yog, 20 tawm tsam 100. Tab sis dab tsi yog tias muaj ntau yam xwm txheej, thiab lawv nyob ze. hais txog? Nyob rau hauv cov ntaub ntawv no, peb yuav tsis xav nyob rau hauv yooj yim, tab sis nyob rau hauv tej yam kev mob tshwm sim. Tus nqi no yog dab tsi thiab yuav suav li cas - qhov no yuav tham hauv peb tsab xov xwm.
Txoj kev xav
Qhov xwm txheej tshwm sim yog lub caij nyoog ntawm ib qho xwm txheej tshwm sim, vim tias lwm qhov xwm txheej cuam tshuam tau tshwm sim lawm. Xav txog ib qho piv txwv yooj yim nrogpov ib npib. Yog tias tseem tsis tau muaj kev kos, ces txoj hauv kev tau txais lub taub hau lossis tails yuav zoo ib yam. Tab sis yog tias tsib zaug ua ke cov nyiaj npib nteg nrog lub tsho tiv no ntawm caj npab, ces pom zoo kom cia siab tias 6th, 7th, thiab ntau dua yog li qhov 10 rov ua dua ntawm qhov tshwm sim zoo li no yuav tsis tsim nyog. Nrog rau txhua qhov rov hais dua, qhov muaj feem ntawm cov tails tshwm tuaj thiab sai lossis tom qab nws yuav poob.
Txoj kev muaj peev xwm ua tau formula
Tam sim no xav seb tus nqi no suav li cas. Cia peb qhia thawj qhov xwm txheej li B, thiab qhov thib ob yog A. Yog tias qhov muaj feem tshwm sim ntawm B txawv ntawm xoom, ces qhov sib npaug hauv qab no yuav siv tau:
P (A|B)=P (AB) / P (B), where:
- P (A|B) – raws li qhov tshwm sim ntawm qhov tshwm sim A;
- P (AB) - qhov tshwm sim ntawm kev sib koom ua ke ntawm cov xwm txheej A thiab B;
- P (B) – qhov tshwm sim ntawm qhov tshwm sim B.
Sib hloov qhov piv no, peb tau P (AB)=P (A | B)P (B). Thiab yog tias peb siv txoj kev induction, ces peb tuaj yeem muab cov khoom tsim tawm thiab siv nws rau tus naj npawb ntawm cov xwm txheej:
P (A1, A2, A3, …A p )=P (A1|A2…Ap )P(A 2|A3…Ap)P (A 3|A 4…Ap)… R (Ap-1 |Ap)R (Ap).
Kev xyaum
Txhawm rau kom nkag siab yooj yim npaum li cas qhov xwm txheej tshwm sim ntawm qhov kev tshwm sim raug suav, cia peb saib ob peb qhov piv txwv. Piv txwv tias muaj ib lub vase uas muaj 8 chocolates thiab 7 mints. Lawv yog cov tib qhov loj thiab random.ob ntawm lawv raug rub tawm ua ntu zus. Yuav ua li cas yog qhov uas lawv ob leeg yuav yog chocolate? Cia peb qhia cov cim. Cia qhov tshwm sim A txhais tau tias thawj cov khoom qab zib yog chocolate, qhov tshwm sim B yog cov khoom qab zib thib ob. Tom qab ntawd koj tau txais cov hauv qab no:
P (A)=P (B)=8 / 15, P (A|B)=P (B|A)=7/14=1/2, P (AB)=8/15 x 1/2=4/15 ≈ 0, 27
Cia peb xav txog ib rooj plaub ntxiv. Xav tias muaj ib tsev neeg muaj ob tug me nyuam thiab peb paub tias tsawg kawg yog ib tug me nyuam yog ib tug ntxhais.
Qhov xwm txheej tshwm sim yog dab tsi uas cov niam txiv no tsis muaj tub? Raws li nyob rau hauv cov ntaub ntawv dhau los, peb pib nrog sau. Cia P(B) yog qhov yuav muaj tsawg kawg yog ib tug ntxhais hauv tsev neeg, P(A|B) yog qhov tshwm sim tias tus menyuam thib ob kuj yog ib tug ntxhais, P(AB) muaj feem yuav muaj ob tug ntxhais hauv tsev neeg. Tam sim no cia peb ua cov kev suav. Nyob rau hauv tag nrho, muaj peev xwm muaj 4 yam sib txawv ntawm kev sib deev ntawm cov me nyuam, thiab nyob rau hauv cov ntaub ntawv no, tsuas yog nyob rau hauv ib rooj plaub (thaum muaj ob tug tub nyob rau hauv tsev neeg), yuav tsis muaj ib tug ntxhais ntawm cov me nyuam. Yog li, qhov tshwm sim P (B)=3/4, thiab P (AB)=1/4. Tom qab ntawd, ua raws li peb cov qauv, peb tau txais:
P (A|B)=1/4: 3/4=1/3.
Qhov tshwm sim tuaj yeem txhais tau raws li hauv qab no: yog peb tsis paub poj niam txiv neej ntawm ib tus menyuam yaus, qhov kev pheej hmoo ntawm ob tus ntxhais yuav yog 25 tawm tsam 100. Tab sis vim peb paub tias ib tus menyuam yog ib tug ntxhais, qhov tshwm sim uas tsev neeg ntawm cov tub tsis muaj, nce mus rau ib feem peb.
