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7.1 Waarskynlikheid: deel 2

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Relatiewe frekwensie vs. Waarskynlikheid

Daar is twee maniere om die waarskynlikheid van enige gebeurtenis van 'n lukrake eksperiment te bepaal:

  1. Bepaal die totale aantal moontlike uitkomstes en bereken die waarskynlikheid deur die definisie te gebruik of
  2. doen die eksperiment en bereken die relatiewe frekwensie van elke uitkomste.

Relatiewe Frekwensie word gedefiniëer as die aantal kere wat 'n gebeurtenis in 'n eksperiment plaasvind, gedeel deur die aantal kere wat die eksperiment gedoen is.

Dit verg 'n baie groot aantal eksperimente voor die relatiewe frekwensie van gebeurtenis gelyk is aan die waarskynlikheid daarvan. Byvoorbeeld: die data in [link] verteenwoordig die uitkomste van 100 proewe van 'n statistieke eksperiment (die gooi van 'n muntstuk 100 keer).

Uitslae van 100 gooie van 'n regverdige muntstuk. K beteken die muntstuk het met sy kop na bo geland en S beteken die muntstuk het met sy stert na bo geland.
K S S K K S K K K K
K K K K S K K S S S
S S K S S K S K S K
K K S S K S S K S S
S K K K S S K S S K
K S S S S K S S K K
S S K S S K S S K S
K S S K S S S S K S
S K S S K K K S K S
S S S K K S S S K S

Die volgende twee voorbeelde wys dat die relatiewe frekwensie van 'n gebeurtenis nie noodwendig gelyk is aan die waarskynlikheid daarvan nie. Relatiewe frekwensie behoort dus eerder beskou te word as 'n benaderde waarskynlikheid.

Bepaal die relatiewe frekwensie wat met elke uitkoms in die volgende data geassosiëer word [link] .

  1. Daar is twee unieke uitkomste: K en S.

  2. Uitkoms Frekwensie
    K 44
    S 56

  3. Die statistieke eksperiment van die muntstuk gooi was 100 keer uitgevoer. Daarom was daar 'n totaal van 100 proewe.

  4. Waarskynlikheid van K = frekwensie van uitkoms aantal proewe = 44 100 = 0 , 44 Relatiewe frekwensie van S = frekwensie van uitkoms aantal proewe = 56 100 = 0 , 56

    Die relatiewe frekwensie van die muntstuk gooie om kop te lewer is 0,44 en die relatiewe frekwensie om stert te lewer is 0,56.

Bepaal die waarskynlikheid van 'n regverdige muntstuk om op enige kant te land.

  1. Daar is twee unieke uitkomste: K en S.

  2. Daar is twee moontlike uitkomste.

  3. Relatiewe Frekwensie van K = aantal gunstige uitkomste totale aantal uitkomste = 1 2 = 0 , 5 Relatiewe Frekwensie van S = aantal gunstige uitkomste totale aantal uitkomste = 1 2 = 0 , 5

    Die waarskynlikheid van 'n regverdige muntstuk om op enige kant te land is 0,5 .

Projek idee

Voer 'n eksperiment uit wat wys dat die relatiewe frekwensie die waarskynlikheid van 'n gegewe uitkoms benader soos wat die aantal proewe toeneem. Doen 10, 20, 50, 100 en 200 proewe van die gooi van 'n muntstuk.

Interpretasie van waarskynlikheidswaardes - (nie in caps, maar ingesluit vir volledigheid)

Die waarskynlikheid van 'n gebeurtenis word dikwels uitgedruk as 'n reële getal tussen 0 en 1, ingesluit. Waar 'n onmoontlike waarskynlikheid deur 0 en 'n versekerde waarskynlikheid deur 1 voorgestel word. Tog is 0 waarskynlikheid gebeure nie altyd onmoontlik nie, terwyl 1 waarskynlikheid gebeure nie altyd verseker is nie. Hierdie subtiele verskil tussen seker en waarskynlikheid 1 word verder bespreek in die gedeelte "amper seker".

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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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