Isibonelo Sombuzo Wengxoxo Ngokungenzeka Kwesenzakalo
Amathuba ayigatsha lezibalo elisetshenziswa kabanzi empilweni yansuku zonke. Amathuba okuba isenzakalo senzeke noma singabi khona angalinganiswa kusetshenziswa umqondo wamathuba. Isihloko esilandelayo sizoxoxa ngezinkinga eziningana eziyizibonelo kanye nengxoxo yazo mayelana namathuba okuba isenzakalo senzeke. Ake sizihlole ngokujulile.
Umbuzo 1: Amathuba Okuvela Kwezinombolo Edayisini
Umbuzo:
Idayi enezinhlangothi eziyisithupha iphonswa kanye. Angakanani amathuba okuthola u-4?
Ingxoxo:
Idayi ejwayelekile inezinhlangothi eziyisithupha: 1, 2, 3, 4, 5, kanye no-6. Uhlangothi ngalunye lunethuba elilinganayo lokuvela. Njengoba sifuna amathuba okugoqa izinombolo ezi-4 kweziyisithupha ezingenzeka, amathuba angabhalwa kanje:
\[ P(4) = \frac{\text{Inani lezindlela ezifunwayo}}{\text{Inani eliphelele lamathuba}} = \frac{1}{6} \]
Ngakho-ke, amathuba okuthola inombolo 4 lapho idayisi iphonswa kanye yi-\(\frac{1}{6}\).
Inkinga 2: Amathuba Ebhokisini Lokudweba
Umbuzo:
Ebhokisini kukhona amabhola abomvu ama-5 namabhola aluhlaza okwesibhakabhaka ama-3. Uma ibhola lidonswa ngokungahleliwe, kungenzeka yini ukuthi ibhola elidonswe libe bomvu?
Ingxoxo:
Inani eliphelele lamabhola ebhokisini yileli:
\[ 5 \text{ (red) } + 3 \text{ (blue) } = 8 \text{ balls } \]
Amabhola esiwafunayo amabhola abomvu, lapho kukhona khona ama-5. Ngakho-ke, amathuba okuthola ibhola elibomvu yilawa:
\[ P(\text{red}) = \frac{\text{Inani lamabhola abomvu}}{\text{Inani eliphelele lamabhola}} = \frac{5}{8} \]
Ngakho-ke, amathuba okukhetha ibhola elibomvu angama-\(\frac{5}{8}\).
Umbuzo 3: Amathuba Amakhanda Enhlamvwini Yemali
Umbuzo:
Uhlamvu lwemali luphonswa kabili. Angakanani amathuba okuthola amakhanda amabili?
Ingxoxo:
Ukuphonswa ngakunye kohlamvu lwemali kunemiphumela emibili engaba khona, okungukuthi amakhanda (H) noma imisila (E). Uma uhlamvu lwemali luphonswa kabili, isikhala sesampula (S) semiphumela engaba khona yilesi:
\[ S = \{(HH), (HE), (EH), (EE)\} \]
Amathuba okuthola amakhanda amabili (HH) angabalwa kanje:
\[ P(HH) = \frac{\text{Inani lemicimbi ye-HH}}{\text{Inani eliphelele lamathuba}} = \frac{1}{4} \]
Ngamanye amazwi, amathuba okuthola amakhanda amabili lapho uhlamvu lwemali luphonswa kabili yi-\(\frac{1}{4}\).
Umbuzo 4: Amathuba Emidlalweni Yamakhadi
Umbuzo:
Kusukela kumakhadi ajwayelekile (amakhadi angu-52), angakanani amathuba okuthola i-Ace of Hearts uma kudonswa ikhadi elilodwa?
Ingxoxo:
Idekhi ejwayelekile yamakhadi inamakhadi angu-52, kufaka phakathi ama-Ace angu-4. Kodwa-ke, sinesithakazelo kuphela ku-Ace of Hearts.
Inani eliphelele lamakhadi angaba khona lingu-52, futhi kukhona i-Ace of Hearts eyodwa kuphela edekhini. Ngakho-ke:
\[ P(\text{Ace of Hearts}) = \frac{\text{Number of Aces of Hearts}}{\text{Total Number of Cards}} = \frac{1}{52} \]
Ngakho-ke, amathuba okudweba i-Ace of Hearts kusuka ku-deck yamakhadi ajwayelekile yi-\(\frac{1}{52}\).
Umbuzo 5: Amathuba Ekudonsweni Kwezimpahla
Umbuzo:
Ku-lottery, kunamathikithi ayi-10, amathathu anemiklomelo kanti ayi-7 angenayo. Uma ithikithi elilodwa lidonswa ngokungahleliwe, angakanani amathuba okuthola umklomelo?
Ingxoxo:
Inani eliphelele lamathikithi liyi-10, kanti inani lamathikithi omklomelo liyi-3. Ngakho-ke, amathuba okuthola ithikithi lomklomelo yilawa:
\[ P(\text{prize}) = \frac{\text{Inani lamathikithi omklomelo}}{\text{Inani eliphelele lamathikithi}} = \frac{3}{10} \]
Ngakho-ke, amathuba okuthola ithikithi lomklomelo yi-\(\frac{3}{10}\).
Umbuzo 6: Amathuba Ebhokisini Leswidi
Umbuzo:
Imbiza iqukethe amaswidi kashokoledi angu-12, amaswidi esitrobheli angu-8, kanye namaswidi ama-mint angu-5. Uma iswidi elilodwa likhethwa ngokungahleliwe, angakanani amathuba okuthola iswidi lemint?
Ingxoxo:
Inani eliphelele lamaswidi ebhodweni yileli:
\[ 12 \text{ (ushokoledi) } + 8 \text{ (strawberry) } + 5 \text{ (mint) } = 25 \text{ amaswidi } \]
Inani lamaswidi e-mint esiwafunayo lingu-5. Ngakho-ke amathuba okuthola amaswidi e-mint yilawa:
\[ P(\text{mint}) = \frac{\text{Number of mints}}{\text{Total number of mints}} = \frac{5}{25} = \frac{1}{5} \]
Ngakho-ke, amathuba okuthola uswidi we-mint angama-\(\frac{1}{5}\).
Umbuzo 7: Amathuba kuLottery
Umbuzo:
Ku-lottery, amabhola ayi-10 anenombolo 1 kuya ku-10 afakwa ebhokisini. Uma kudonswa ibhola elilodwa, angakanani amathuba okuthola inombolo elinganayo?
Ingxoxo:
Inani eliphelele lamabhola lingu-10 kanti izinombolo ezilinganayo phakathi kwawo zingu-2, 4, 6, 8, kanye no-10, okuyisibalo samabhola ama-5.
Ngakho-ke amathuba okuthola inombolo elinganayo yilawa:
\[ P(\text{even}) = \frac{\text{Inani lezinombolo ezilinganayo}}{\text{Inani eliphelele lamabhola}} = \frac{5}{10} = \frac{1}{2} \]
Ngakho-ke, amathuba okuthola inombolo elinganayo yi-\(\frac{1}{2}\).
Umbuzo 8: Amathuba Omdlalo
Umbuzo:
Emdlalweni webhasikidi, umdlali unethuba elingu-0,7 lokushaya iphuzu ebholeni ngalinye. Uma umdlali eshaya ishothi eli-1, angakanani amathuba okuthi angaphuthelwa?
Ingxoxo:
Amathuba okuthola iphuzu ngempumelelo angu-0,7. Ngakho-ke, amathuba okwehluleka ukuthola iphuzu yilawa:
\[ P(\text{failed}) = 1 – P(\text{succeeded}) = 1 – 0,7 = 0,3 \]
Ngakho-ke, ithuba lokuthi umdlali ahluleke ukuthola iphuzu elilodwa ngokuphonsa okukodwa lingu-0,3 noma u-30%.
Ngemva kokuhlola izibonelo nezingxoxo ezingenhla, singaqonda ukuthi umqondo wamathuba usetshenziswa kanjani ezimweni nasezimweni ezahlukahlukene. Lokhu kuqonda kungasiza ekuxazululeni izinkinga zansuku zonke ezihilela ukungaqiniseki nokulinganisa, futhi kunikeze isisekelo esiqinile sezinhlelo ezengeziwe zokutadisha izibalo kanye namathuba.
