Zitsanzo za Mafunso Okhudza Lamulo Lowonjezera Zochitika Ziwiri A ndi B Zomwe Sizili Zosiyana
Pendauluan
Pa kuthekera, kumvetsetsa mfundo zoyambira ndi momwe zimagwiritsidwira ntchito ndikofunikira kwambiri. Lingaliro limodzi lomwe limabwera nthawi zambiri ndi lamulo la kuwonjezera kuthekera. M'nkhaniyi, tifufuza mozama lamulo la kuwonjezera pa zochitika ziwiri zomwe sizili zapadera. Zochitika zomwe sizili zapadera zimachitika pamene zochitika ziwiri zimagawana chinthu chimodzi chotheka, kapena mwanjira ina, zochitika zonse ziwiri zimatha kuchitika nthawi imodzi. Kuti timvetsetse bwino, tiyeni tiwone chitsanzo cha vuto ndi kufotokozera kwake.
Chiphunzitso Choyambira
Ngati tili ndi zochitika ziwiri A ndi B zomwe sizikugwirizana, ndiye kuti lamulo lowonjezera powerengera mwayi wa chochitika A kapena B likhoza kufotokozedwa motere:
\[ P(A \chikho B) = P(A) + P(B) – P(A \chikho B) \]
Pano:
– \( P(A \cup B) \) ndi mwayi woti A kapena B (kapena zonse ziwiri) zichitike.
– \( P(A) \) ndi mwayi woti chochitika A chichitike.
– \( P(B) \) ndi mwayi woti chochitika B chichitike.
– \( P(A \cap B) \) ndi mwayi woti A ndi B zichitike nthawi imodzi.
Chitsanzo cha mavuto
Funso 1: Mu sukulu, ophunzira 70% amakonda kusewera mpira (chochitika A), ophunzira 40% amakonda kusewera basketball (chochitika B), ndipo ophunzira 20% amakonda kusewera masewera onse awiri. Kodi mwayi woti wophunzira azisewera mpira kapena basketball ndi wotani?
Kukambirana:
Ndizodziwika kuti:
– \( P(A) = 0.70 \)
– \( P(B) = 0.40 \)
– \( P(A \cap B) = 0.20 \)
Kugwiritsa ntchito lamulo lowonjezera zochitika ziwiri zomwe sizigwirizana:
\[ P(A \chikho B) = P(A) + P(B) – P(A \chikho B) \]
\[ P(A \chikho B) = 0.70 + 0.40 – 0.20 \]
\[ P(A \chikho B) = 0.90 \]
Kotero, mwayi woti wophunzira amakonda kusewera mpira kapena basketball ndi 0.90 kapena 90%.
Funso 2: Mu kafukufuku, 35% ya omwe adayankha amakonda khofi (chochitika A), 50% ya omwe adayankha amakonda tiyi (chochitika B), ndipo 10% ya omwe adayankha amakonda zonse ziwiri. Kodi pali mwayi wotani woti woyankhayo amakonda khofi kapena tiyi?
Kukambirana:
Ndizodziwika kuti:
– \( P(A) = 0.35 \)
– \( P(B) = 0.50 \)
– \( P(A \cap B) = 0.10 \)
Kugwiritsa ntchito lamulo lowonjezera zochitika ziwiri zomwe sizigwirizana:
\[ P(A \chikho B) = P(A) + P(B) – P(A \chikho B) \]
\[ P(A \chikho B) = 0.35 + 0.50 – 0.10 \]
\[ P(A \chikho B) = 0.75 \]
Kotero, mwayi woti woyankhayo angakonde khofi kapena tiyi ndi 0.75 kapena 75%.
Funso 3: Kuchokera ku ziwerengero, zimadziwika kuti anthu 60% amakonda kuwerenga mabuku (chochitika A), anthu 30% amakonda kuonera mafilimu (chochitika B), ndipo anthu 15% amakonda kuchita zonse ziwiri. Kodi pali mwayi wotani woti munthu azikonda kuwerenga mabuku kapena kuonera mafilimu?
Kukambirana:
Ndizodziwika kuti:
– \( P(A) = 0.60 \)
– \( P(B) = 0.30 \)
– \( P(A \cap B) = 0.15 \)
Kugwiritsa ntchito lamulo lowonjezera zochitika ziwiri zomwe sizigwirizana:
\[ P(A \chikho B) = P(A) + P(B) – P(A \chikho B) \]
\[ P(A \chikho B) = 0.60 + 0.30 – 0.15 \]
\[ P(A \chikho B) = 0.75 \]
Kotero, mwayi woti munthu amakonda kuwerenga mabuku kapena kuonera mafilimu ndi 0.75 kapena 75%.
Funso 4: Kuchokera ku kafukufuku wina ku lesitilanti, 55% ya makasitomala adaitanitsa pizza (chochitika A), 35% ya makasitomala adaitanitsa pasitala (chochitika B), ndipo 20% ya makasitomala adaitanitsa zonse ziwiri. Kodi pali mwayi wotani woti kasitomala ayitanitsa pizza kapena pasitala?
Kukambirana:
Ndizodziwika kuti:
– \( P(A) = 0.55 \)
– \( P(B) = 0.35 \)
– \( P(A \cap B) = 0.20 \)
Kugwiritsa ntchito lamulo lowonjezera zochitika ziwiri zomwe sizigwirizana:
\[ P(A \chikho B) = P(A) + P(B) – P(A \chikho B) \]
\[ P(A \chikho B) = 0.55 + 0.35 – 0.20 \]
\[ P(A \chikho B) = 0.70 \]
Kotero, mwayi woti kasitomala agule pizza kapena pasitala ndi 0.70 kapena 70%.
Mapeto
Pophunzira kuthekera, lamulo lowonjezera zochitika ziwiri zomwe sizili zapadera A ndi B ndilofunika kwambiri kuti mudziwe kuthekera kwa chochitika chimodzi kapena zonse ziwiri kuchitika nthawi imodzi. Kugwiritsa ntchito fomula \( P(A \cup B) = P(A) + P(B) – P(A \cap B) \) kumapangitsa kuti zikhale zosavuta kuwerengera kuthekera kolumikizana kwa zochitika ziwiri zomwe zili ndi malo olumikizirana kapena chinthu chofanana.
Kudzera mu zitsanzo zomwe zili pamwambapa, titha kuwona kuti kumvetsetsa masitepe oyambira a kuwerengera kumeneku kumatithandiza kukugwiritsa ntchito pazochitika zosiyanasiyana, kaya pamaphunziro, kafukufuku, kapena moyo watsiku ndi tsiku. Kumveka bwino komanso kulondola pozindikira zomwe zikuchitika ndi zinthu zomwe zimagawana ndizofunikira kwambiri pakuwerengera bwino mwayi. Chifukwa chake, kuchita zinthu mosasinthasintha komanso kumvetsetsa mfundo zoyambira kudzathandiza kwambiri pakudziwa bwino nkhaniyi.
