Yuav ua li cas yog lub zwj ceeb tshwm sim thiab yuav ua li cas xam nws raug?

Feem ntau nyob rau hauv peb lub neej peb yuav ntsib nrog lub fact tias koj yuav tsum ntsuam xyuas cov uas yuav muaj qhov tshwm sim ntawm tej kev tshwm sim. Kuv yuav tsum tau yuav ib tug lottery ticket los yog tsis, yuav hauv pem teb ntawm peb tus me nyuam nyob rau hauv lub tsev neeg, seb puas los yog tag kis pos huab los nag dua - xws piv txwv yog countless. Nyob rau hauv lub nyuaj cov ntaub ntawv, cov xov tooj ntawm dej siab tau muab faib los ntawm tag nrho cov ntawm cov txheej xwm. Yog hais tias lub lottery ticket winning 10, thiab ib tug tag nrho ntawm 50, qhov uas yuav tau txais tus nqi zog sib npaug zos rau 10/50 = 0.2, piv txwv li 20 tiv tiag 100. Tab sis yuav ua li cas nyob rau hauv cov kev tshwm sim hais tias muaj ntau yam txheej xwm, thiab lawv yuav zoo txog rau ib leeg? Nyob rau hauv cov ntaub ntawv no, peb xav nyob rau hauv tsis yog ib qho yooj yim, thiab lub zwj ceeb tshwm sim. Yuav ua li cas hom ntawm cov nqi thiab yuav ua li cas nws yuav tsum xam - nws yuav cia li yuav them nyob rau hauv no tsab xov xwm.

notion

Conditional probability - ib lub caij nyoog tshwm sim ntawm ib tug kev tshwm sim, muab hais tias cov lwm yam kev tshwm sim uas txuam nrog nws twb tshwm sim. Xav txog ib tug piv txwv yooj yim ntawm ntuav ib npib nyiaj. Thaum kos yog tsis muaj, ces tus yuav ntog taub hau los yog tails yuav tau tib yam. Tab sis yog hais tias tus npib tsib lub sij hawm nyob rau hauv ib tug kab mus rau hauv tej caj npab thiab cia siab tias yuav pom zoo lub 6, 7, thiab tshwj xeeb tshaj yog lub 10 repetition ntawm xws li ib lub sij hawm yuav tsis thwj. Nrog txhua rov lub sij hawm tsis ntawm ib tug dav dawb hau, qhov uas yuav ntawm tails yog loj hlob, thiab ua ntej los yog tom qab ntawd nws yuav tseem poob.

Cov mis ntawm conditional probability

Cia peb tam sim no nrog yuav ua li cas no tus nqi yog payment. Peb txhais los ntawm B thawj tshwm sim thiab lub thib ob los ntawm A. Yog hais tias qhov uas yuav muaj tshwm sim nyob rau hauv qhov uas tsis yog-xoom, ces nws yog kev ncaj ncees rau cov nram no kab zauv:

P (A | B) = P (AB) / P (B), nyob rau:

• P (A | B) - Ib tug tag nrho ntawm conditional probability;
• P (AB) - qhov tshwm sim ntawm co-cuam ntawm cov txheej xwm A thiab B;
• P (B) - qhov tshwm sim ntawm cov kev tshwm sim B.

Me ntsis hloov tau tus piv P (AB) = P (A | B) P * (B). Thiab yog hais tias peb thov cov qauv ntawm cov induction, nws tseem tau mus deduce cov mis ntawm cov khoom thiab siv nws rau ib arbitrary tus naj npawb ntawm cov txheej xwm:

R (A _{1, 2,} A _3, ... A _n) = P (A ₁ | A ₂ ... Ib tug _n) * P ₍₂ | A ₃ ... Ib tug _n) * P ₍₃ | _A4 ... Ib tug _n ) ... P _(n-1 | _n A) * P _(n).

xyaum

Kom nws yooj yim dua mus rau nrog yuav ua li cas lub xam zwj ceeb tshwm sim rau ib tug kev tshwm sim, xav txog ib tug ob peb tus piv txwv. Piv txwv muaj ib lub tais nyob rau hauv uas muaj 8 7 chocolates thiab mint. Lawv yog cov tib nyob rau hauv loj thiab across consecutively rho tawm ob ntawm lawv. Yuav ua li cas yog qhov uas yuav hais tias ob leeg yuav tsum chocolate? Peb paub cov cim. Thiab cia cov txhais tau tias cov thawj qhob noom xim kasfes khoom qab zib, ib tug tag nrho ntawm Nyob rau hauv - lub thib ob qab zib chocolate. Tom qab ntawd peb tau txais lub nram 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

Xav txog lwm cov ntaub ntawv. Xav tias koj muaj ib tug ob-tus me nyuam tsev neeg, thiab peb paub tias tsawg kawg yog ib tus me nyuam yog ib tug hluas nkauj. Yuav ua li cas yog lub zwj ceeb tshwm sim tias tus tub hluas nyob rau hauv cov niam txiv tsis tau? Raws li nyob rau hauv lub yav dhau los cov ntaub ntawv, cia tus pib nrog ib co cim. Cia P (B) - qhov tshwm sim hais tias ib tsev neeg muaj tsawg kawg yog ib tug hluas nkauj, P (A | B) - qhov tshwm sim tias tus thib ob tus me nyuam kuj yog ib tug hluas nkauj, F (AB) - txoj hais tias ib tug neeg ntawm ob tug hluas nkauj. Tam sim no peb ua cov lus teb. Muaj yuav ua tau 4 txawv ob peb ua ke ntawm txiv neej thiab poj niam me nyuam thiab nyob rau tib lub sij hawm nyob rau hauv tsuas yog ib qho ntaub ntawv (thaum lub tsev ob tug hluas), hluas nkauj yuav tsis muaj ntawm cov me nyuam. Yog li ntawd, qhov yuav tshwm P (B) = 3/4 thiab P (AB) = 1/4. Ces ua raws li peb cov mis mos, peb tau txais:

P (A | B) = 1/4: 3/4 = 1/3.

Txhais cov yuav ua tau li no: yog hais tias peb twb tsis tau siv yog paub txog lub teb ntawm ib qho ntawm cov me nyuam, qhov uas yuav muaj ob tug hluas nkauj yuav tsum 25 tiv thaiv 100. Tab sis txij thaum peb paub hais tias ib tug me nyuam yog ib tug hluas nkauj, lub qhov muaj tseeb hais tias cov tub hluas nyob rau hauv lub tsev neeg tsis muaj ib tug nce mus rau feem peb.