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Onderling uitsluitende gebeurtenisse

Onderling uitsluitende gebeurtenisse is gebeurtenisse wat nie op dieselfde tyd waar kan waar wees nie.

Voorbeelde van onderling uitsluitende gebeure is:

  1. 'n Dobbelsteen wat op 'n ewe of op 'n onewe getal land.
  2. 'n Student wat 'n eksamen dop of slaag.
  3. 'n Muntstuk wat op kop of stert land

Dit beteken dat as ons die elemente ondersoek wat die stelle A en B opmaak, sal daar geen gemeenskaplike elemente wees nie. Daarom, A B = (waar verwys na die leë stel). Since, P ( A B ) = 0 , vergelyking [link] word:

P ( A B ) = P ( A ) + P ( B )

vir onderling uitsluitende gebeurtenisse.

Ons kan onderling uitsluitende gebeurtenisse op 'n Venn-diagram voorstel. In hierdie geval raak die twee sirkels nie aan mekaar raak, maar is eerder heeltemal aparte dele van die steekproefruimte.

Venn diagram vir onderlinge uitsluitende gebeurtenisse

Oefeninge met onderling uitsluitende gebeutrenisse

  1. 'n Boks bevat gekleurde blokkies. Die aantal van elke kleur word deur die volgende tabel voorgestel.
    Kleur Pers Oranje Wit Pienk
    Aantal blokkies 24 32 41 19
    'n Blokkie word ewekansig gekies. Wat is die waarskynlikheid dat die blokkie:
    1. pers
    2. pers of wit is
    3. pienk en oranje is
    4. nie oranje is nie?
  2. 'n Klein private skool het' n klas met kinders van verskillende ouderdomme. Die tabel gee die aantal leerlinge van elke ouderdomsgroep in die klas.
    3 jarige meisies 3 jarige seuns 4 jarige meisies 4 jarige seuns 5 jarige meisies 5 jarige seuns
    6 2 5 7 4 6
    As 'n leerder lukraak gekies word, wat is die waarskynlikheid dat dat die leerder:
    1. 'n meisie is
    2. 'n 4 jarige seun is
    3. 3 of 4 jaar oud is
    4. 3 en 4 jaar oud is
    5. nie 5 jaar oud is nie
    6. 3 jaar oud of 'n meisie is?
  3. Fiona het 85 gemerkte skyfies wat genommer is vanaf 1 tot 85. As 'n skyfie lukraak gekies word, wat is die waarskynlikheid dat die nommer van die skyfie:
    1. eindig met 'n 5
    2. met 3 vermenigvuldig kan word
    3. met 6 vermenigvuldig kan word
    4. die nommer 65 is
    5. nie 'n veelvoud van 5 is nie
    6. 'n veelvoud van 4 of 3 is
    7. 'n veelvoud van 2 en 6 is
    8. die nommmer 1 is?

Komplementêre gebeurtenisse

Die waarskynlikheid van komplementêre gebeurtenis verwys na die waarskynlikheid dat gebeure nie sal plaasvind nie. Byvoorbeeld: as P ( A ) = 0 . 25 , dan is die warskynlikheid dat A nie gebeur nie dieselfde as die waarskynlikheid dat al die ander gebeure in S gebeur minus as die waarskynlikheid dat A gebeur. Dit beteken dat

P ( A ' ) = 1 - P ( A )

waar A' verwys na `nie A' Met ander woorde, die waarskynlikheid van `nie A' is gelyk aan een minus die waarskynlikheid van A.

As jy twee dobbelstene gooi, een rooi en die ander blou, wat is die waarskynlikheid dat ten minste een van hulle 'n ses sal wees?

  1. Om hierdie tipe probleem op te los, bereken die waarskynlikheid dat daar geen 6 sal wees nie.

  2. Die waarskynlikheid dat die rooi dobbelsteen nie 'n 6 is nie is 5/6 en die waarskynlikheid dat die bloue nie 'n 6 is nie, is ook 5/6.

  3. So die waarskynlikheid dat geeneen 'n ses sal wees nie is 5 / 6 × 5 / 6 = 25 / 36 .

  4. So die waarskynlikheid dat ten minste een 'n 6 sal wees is 1 - 25 / 36 = 11 / 36 .

'n Sak bevat drie rooi balle, vyf wit balle, twee groen balle en vier blou balle:

1. Bereken die waarskynlikheid dat 'n rooi bal getrek word.

2. Bereken die waarskynlikheid dat 'n bal wat nie rooi is nie getrek word.

  1. Laat R die gebeurtenis waar 'n rooi bal getrek word wees:

    • P(R)-n(R)/n(S)=3/14
    • R en R' is komplementêre gebeure.
  2. P(R') = 1 - P(R) = 1 -3/14 = 11/14

    • Alternatiewelik P(R') = P(B) + P(W) + P(G)
    • P(R') = 4/14 + 5/14 + 2/14 = 11/14

Ewekansige eksperimente

  • S = { heel getalle vanaf 1 tot 16 } , X = { ewe getalle vanaf 1 tot 16 } en Y = { priemgetalle vanaf 1 tot 16 }
    1. Teken 'n Venn-diagram S , X en Y .
    2. Skryf neer n ( S ) , n ( X ) , n ( Y ) , n ( X Y ) , n ( X Y ) .
    Klik hier vir die oplossing.
  • Daar is 79 Graad 10 leerders by die skool. Almal van hulle neem Wiskunde, Aardrykskunde of Geskiedenis. Die aantal wat Aardrykskunde neem is 41, die wat Geskiedenis neem is 36 en 30 neem Wiskunde. Die aantal wat Wiskunde en Geskiedenis neem is 16; die aantal wat Geskiedenis en Aardrykskunde neem is 6. Dan is daar 8 wat slegs Wiskunde en 16 wat slegs Geskiedenis neem.
    1. Teken 'n Venn-diagram om al die inligting voor te stel.
    2. Hoeveel leerders neem Wiskunde en Aardrykskunde, maar nie Geskiedenis nie?
    3. Hoeveel leerders neem slegs Aardrykskunde?
    4. Hoeveel leerders neem al drie hierdie vakke?
    Klik hier vir die oplossing.
  • Stukkies papier met die getalle 1 tot 12 word in 'n boks geplaas en die boks word geskud. Een stukkie papier word getrek en dan terug geplaas.
    1. Wat is die steekproefruimte, S ?
    2. Skryf die versameling A neer, wat die gebeurtenis om 'n faktor van 12 te trek, voorstel.
    3. Skryf die versameling B neer, wat die gebeurtenis om 'n priemgetal te trek, voorstel.
    4. Doen nou 'n voorstelling van A , B en S deur middel van 'n Venn-diagram.
    5. Skryf die volgende neer:
      1. n ( S )
      2. n ( A )
      3. n ( B )
      4. n ( A B )
      5. n ( A B )
    6. Is n ( A B ) = n ( A ) + n ( B ) - n ( A B ) ?
    Klik hier vir die oplossing.

Questions & Answers

What is price elasticity of demand and its degrees. also explain factors determing price elasticity of demand?
Yutansh Reply
Price elasticity of demand (PED) is use to measure the degree of responsiveness of Quantity demanded for a given change on price of the good itself, certis paribus. The formula for PED = percentage change in quantity demanded/ percentage change in price of good A
GOH
its is necessarily negative due to the inverse relationship between price and Quantity demanded. since PED carries a negative sign most of the time, we will usually the absolute value of PED by dropping the negative sign.
GOH
PED > 1 means that the demand of the good is price elasticity and for a given increase in price there will be a more then proportionate decrease in quantity demanded.
GOH
PED < 1 means that the demand of the good is price inelasticity and for a given increase in price there will be a less then proportionate decrease in quantity demanded.
GOH
The factors that affects PES are: Avaliablilty of close substitutes, proportion of income spent on the good, Degree of necessity, Addiction and Time.
GOH
Calculate price elasticity of demand and comment on the shape of the demand curve of a good ,when its price rises by 20 percentage, quantity demanded falls from 150 units to 120 units.
Helen Reply
5 %fall in price of good x leads to a 10 % rise in its quantity demanded. A 20 % rise in price of good y leads to do a 10 % fall in its quantity demanded. calculate price elasticity of demand of good x and good y. Out of the two goods which one is more elastic.
Helen
what is labor
Grace Reply
labor is any physical or mental effort that helps in the production of goods and services
Kwabena
what is profit maximizing level of out put for above hypothetical firm TC = Q3 - 21Q2 + 600 + 1800 P = 600 MC = 3Q2 - 42Q + 600
Sosna Reply
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
Sosna
sorry it the mistake answer it is question
Sosna
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
Sosna
The formula for calculation income elasticity of demand is the percent change in quantity demanded divided by the percent change in income.
Sosna
what is labor productivity
Lizzy Reply
if the demand function is q=25-4p+p² 1.find elasticity of demand at the point p=5?
Puja Reply
what are some of the difference between monopoly and perfect competition market
Obeng Reply
n a perfectly competitive market, price equals marginal cost and firms earn an economic profit of zero. In a monopoly, the price is set above marginal cost and the firm earns a positive economic profit. Perfect competition produces an equilibrium in which the price and quantity of a good is economic
Naima
what are some characteristics of monopoly market
Obeng Reply
explicit cost is seen as a total experiences in the business or the salary (wages) that a firm pay to employee.
Idagu Reply
what is price elasticity
Fosua
...
krishna
it is the degree of responsiveness to a percentage change in the price of the commodity
Obeng
economics is known to be the field
John Reply
what is monopoly
Peter Reply
what is taxation
Peter
is the compulsory transfer of wealth from the private sector to the public sector
Jonna
why do monopoly make excess profit in both long run and short run
Adeola Reply
because monopoly have no competitor on the market and they are price makers,therefore,they can easily increase the princes and produce small quantity of goods but still consumers will still buy....
Kennedy
how to identify a perfect market graph
Adeola Reply
what is the investment
jimmy
investment is a money u used to the business
Mohamed
investment is the purchase of good that are not consumed today but are used in the future to create wealth.
Amina
investment is the good that are not consumed
Fosua
What is supply
Fosua
 Supply represents how much the market can offer.
Yusif
it is the quantity of commodity producers produces at the market
Obeng
what is the effect of scarce resources on producers
Phindu Reply
explain how government taxes and government producer subsidies affect supply
Chanda
what is economic
Charles Reply
what are the type of economic
Charles
macroeconomics,microeconomics,positive economics and negative economics
Gladys
what are the factors of production
Gladys
process of production
Mutia
Basically factors of production are four (4) namely: 1. Entrepreneur 2. Capital 3. Labour and; 4. Land but there has been a new argument to include an addition one to the the numbers to 5 which is "Technology"
Elisha
what is land as a factor of production
Gladys
what is Economic
Abu
economics is how individuals bussiness and governments make the best decisions to get what they want and how these choices interact in the market
Nandisha
Economics as a social science, which studies human behaviour as a relationship between ends and scarce means, which have alternative uses.
Yhaar
Economics is a science which study human behaviour as a relationship between ends and scarce means
John
Economics is a social sciences which studies human behavior as a relationship between ends and scarce mean, which have alternative uses.....
Pintu
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
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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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