Su'aalo Tusaale ah oo Ka Hadlaya Suurtagalnimada Dhacdooyinka Isku-dhafan
Hordhac ku saabsan Suurtagalnimada Dhacdooyinka Isku-dhafan
Suurtagalnimada waa laan xisaabeed oo dareysa suurtagalnimada dhacdo dhacda. Suurtagalnimada dhacdo isku dhafan waa suurtogalnimada dhacdo ku lug leh wax ka badan hal dhacdo. Tusaale ahaan, suurtogalnimada in tiro siman lagu rogo laadhuu iyo ace laga soo qaado sagxad kaararka ciyaarta ah waa tusaalooyin dhacdooyin isku dhafan. Maqaalkani wuxuu ka hadli doonaa dhowr dhibaato oo tusaale ah wuxuuna ka hadli doonaa suurtagalnimada dhacdooyinka isku dhafan.
Fikradda Aasaasiga ah ee Suurtagalnimada Dhacdooyinka Isku-dhafan
Waxaa jira laba nooc oo dhacdooyin isku dhafan ah:
1. Dhacdooyin Isku-dhafan oo Gaar ah: Laba dhacdo oo aan isku mar dhici karin. Tusaale ahaan, marka la rogrogayo laadhuu, dhacdooyinka rogidda laadhuuga 2 iyo 5 waa dhacdooyin isku-dhafan sababtoo ah ma suurtowdo in labada tiroba la rogo isku mar.
2. Dhacdooyin aan is-dhaafsi lahayn: Laba dhacdo oo isku mar dhici kara. Tusaale ahaan, sawir-qaadista kaararka ciyaarta, dhacdooyinka helitaanka kaarka wadnaha (♥) iyo kaarka lambarka 10 waa dhacdooyin aan is-dhaafsi lahayn sababtoo ah waxaa jira kaadh wadnaha oo lambarkiisu yahay 10.
Waa kuwan qaacidooyin aasaasi ah oo loo isticmaalo xisaabinta suurtagalnimada dhacdooyinka isku dhafan:
– P(A ama B) (dhacdooyinka aan labada dhinac ahayn): \(P(A \cup B) = P(A) + P(B) – P(A \cap B)\)
– P(A ama B) (dhacdooyinka labada dhinac u gaar ah): \(P(A \cup B) = P(A) + P(B)\)
– P(A iyo B) (dhacdooyinka madax-bannaan): \(P(A \cap B) = P(A) \times P(B)\)
Su'aalo iyo Doodo Tusaale ah
Su'aal Tusaale 1aad: Laadhuu
Su'aal:
Waa maxay fursadda lagu heli karo tiro siman ama tiro ka weyn 4 marka la isticmaalayo laydh?
Dood:
Marka hore, aan qeexno dhacdooyinka:
– Dhacdada A: Helitaanka lambar siman (2, 4, 6)
– Dhacdada B: Helitaanka tiro ka badan 4 (5, 6)
Marka xigta, waxaan go'aamineynaa suurtogalnimada dhacdo kasta:
– \(P(A) = \frac{3}{6} = \frac{1}{2}\)
– \(P(B) = \frac{2}{6} = \frac{1}{3}\)
Maadaama ay jirto tiro 6 ah oo ku jirta labada dhacdo ee A iyo B, waxaan u baahanahay inaan xisaabino \(P(A \cap B)\):
– \(P(A \cap B) = \frac{1}{6}\) (sababtoo ah hal lambar oo keliya, oo ah 6, ayaa ku jira A iyo B labadaba)
Adigoo adeegsanaya qaacidada dhacdooyinka aan isku-dhafanayn:
\[P(A \koob B) = P(A) + P(B) – P(A \koob B) = \frac{1}{2} + \frac{1}{3} – \frac{1}{6}\]
Aan isku mid ka dhigno jajabyadan:
\[P(A \koob B) = \frac{3}{6} + \frac{2}{6} – \frac{1}{6} = \frac{4}{6} = \frac{2}{3}\]
Markaa, fursadda helitaanka tiro siman ama tiro ka weyn 4 waa \(\frac{2}{3}\).
Su'aal Tusaale 2: Ciyaarista Kaararka
Su'aal:
Waa maxay fursadda lagu heli karo Ace ama spade ka mid ah kaararka ciyaarta?
Dood:
Marka hore, aan qeexno dhacdooyinka:
– Dhacdada A: Helitaanka kaarka Ace (4 wadar ahaan, mid ka mid ah suudh kasta)
– Dhacdada B: Helitaanka kaarka spade (wadarta guud 13)
Marka xigta, waxaan go'aamineynaa suurtogalnimada dhacdo kasta:
– \(P(A) = \frac{4}{52} = \frac{1}{13}\)
– \(P(B) = \frac{13}{52} = \frac{1}{4}\)
Maadaama Ace of Spades lagu daray labada dhacdo ee A iyo B, waxaan u baahanahay inaan xisaabino \(P(A \cap B)\):
– \(P(A \cap B) = \frac{1}{52}\)
Adigoo adeegsanaya qaacidada dhacdooyinka aan isku-dhafanayn:
\[P(A \koob B) = P(A) + P(B) – P(A \koob B) = \frac{1}{13} + \frac{1}{4} – \frac{1}{52}\]
Aan isku mid ka dhigno jajabyadan:
\[
P(A \koob B) = \frac{4}{52} + \frac{13}{52} – \frac{1}{52} = \frac{16}{52} = \frac{4}{13}
\]
Markaa, fursadda helitaanka Ace ama spade waa \(\frac{4}{13}\).
Tusaale ahaan Dhibaatada 3aad: Kubbad Sanduuq ku jirta
Su'aal:
Sanduuq waxaa ku jira 3 kubbadood oo cas, 4 kubbadood oo buluug ah, iyo 5 kubbadood oo cagaaran. Haddii hal kubbad si aan kala sooc lahayn loo sawiro, waa maxay fursadda lagu heli karo kubad cas ama kubad cagaaran?
Dood:
Marka hore, aan qeexno dhacdooyinka:
– Dhacdada A: Helitaanka kubad cas (lambarka 3)
– Dhacdada B: Helitaanka kubad cagaaran (lambarka 5)
Marka xigta, waxaan go'aamineynaa suurtogalnimada dhacdo kasta:
– Wadarta tirada kubbadaha = 3 + 4 + 5 = 12
– \(P(A) = \frac{3}{12} = \frac{1}{4}\)
– \(P(B) = \frac{5}{12}\)
Maadaama aysan jirin kubad isku mar noqon karta casaan iyo cagaar, dhacdooyinkani waa kuwo isku mid ah:
\[P(A \koob B) = P(A) + P(B) = \frac{1}{4} + \frac{5}{12}\]
Aan isku mid ka dhigno jajabyadan:
\[
P(A \koob B) = \frac{3}{12} + \frac{5}{12} = \frac{8}{12} = \frac{2}{3}
\]
Markaa, fursadda helitaanka kubbadda cas ama kubbadda cagaaran waa \(\frac{2}{3}\).
Tusaale Su'aal 4: Laba Lacagood
Su'aal:
Haddii laba qadaadiic isku mar la tuuro, waa maxay fursadda ugu yaraan hal madax uu soo muuqan karo?
Dood:
Waxaan qeexeynaa Dhacdada A: la kulanka ugu yaraan hal sawir.
Waxaa jira afar natiijo oo suurtagal ah oo ka dhalan karta tuurista laba qadaadiic:
1. HH
2. HT
3. TH
4. TT
Dhacdooyinka ay ku jiraan ugu yaraan hal sawir waa:
– HT
– TH
– TT
Aan xisaabino suurtogalnimada mid kasta:
– Tirada dhacdooyinka suurtagalka ah (wadarta): 4
– Tirada dhacdooyinka oo ka kooban ugu yaraan hal sawir: 3
\[
P(A) = \frac{Tirada dhacdooyinka leh ugu yaraan hal madax} Wadarta tirada dhacdooyinka} = \frac{3}{4}
\]
Markaa, fursadda ugu yaraan hal sawir oo soo muuqanaya waa \(\frac{3}{4}\).
Gabagabo
Doodda dhibaatooyinka kor ku xusan waxay muujinaysaa sida aan u xisaabin karno suurtagalnimada dhacdo isku dhafan, ha ahaato mid isku dhafan ama mid aan isku mid ahayn. Annagoo fahmayna fikradaha aasaasiga ah iyo adeegsiga qaacidooyinka saxda ah, waxaan go'aamin karnaa suurtagalnimada isku-darka dhacdooyinka qaarkood ee ka dhaca xaalado maalinle ah oo kala duwan. Sii wad ku celcelinta xirfadahaaga dhibaatooyin kala duwan si aad u noqoto mid aad ugu xeel dheer go'aaminta suurtagalnimada dhacdooyinka isku dhafan.
