Ka Pahiki o nā Hanana Hui: Manaʻo a me ka Hoʻohana ʻana ma nā ʻĀpana like ʻole
Pendahuluan
He lālā koʻikoʻi loa ka probability o ka makemakika a hoʻohana pinepine ʻia i ke ola o kēlā me kēia lā. Ma kēia ʻatikala, e kūkākūkā mākou i ka probability o nā hanana hui, nona nā noi like ʻole ma nā ʻano like ʻole e like me ka hoʻokele waiwai, nā helu helu, nā ʻepekema pilikanaka, a me ka ʻepekema. ʻO ka probability hui kahi manaʻo i hoʻohana ʻia e hoʻoholo i ka likelike o nā hanana a i ʻole nā hanana e hana like ana. E wehewehe kikoʻī kēia ʻatikala i ke kumumanaʻo kumu o ka probability hui, kona mau ʻano, a me kāna mau noi ma ke ola maoli.
Ka Wehewehena o ka Pahiki o nā Hanana Hui
ʻO ka likelika o kahi hanana hui ʻo ia ka likelika o nā hanana he nui ma kahi hoʻokolohua. Ma ke kumumanaʻo likelika, hiki ke helu ʻia ka likelika o kahi hanana hui me ka hoʻohana ʻana i kekahi mau lula kumu, ma muli o ke ʻano o ka pilina ma waena o nā hanana. Aia ʻelua ʻano nui o nā pilina hanana i noʻonoʻo pinepine ʻia i ka wā e helu ai i ka likelika o kahi hanana hui: nā hanana kūʻokoʻa like ʻole a me nā hanana kūʻokoʻa.
Nā Hanana Kūʻokoʻa like ʻole
ʻO nā hanana kūʻokoʻa like ʻole nā hanana i hiki ʻole ke hana like. No ka laʻana, i ka wā e ʻōwili ana i kahi dice, ʻo ka helu e kū mai ana ma ka ʻaoʻao luna ʻo ia kekahi o nā helu 1 a hiki i ka 6. No laila, inā ʻo ka hanana o ka ʻōwili ʻana i ka 3 kekahi o nā hanana o ka ʻōwili ʻana i ka 5, a laila ʻaʻole hiki i ka hanana o ka ʻōwili ʻana i ka 5 ke hana like.
ʻO ka ikaika nui o nā hanana kūʻokoʻa like ʻole, ʻo ia ka hiki ke hui pū ʻia o ʻelua mau hanana kūʻokoʻa like ʻole ka huina o nā hiki o kēlā me kēia o nā hanana ʻelua. Ma ke ʻano makemakika, inā he mau hanana kūʻokoʻa like ʻole ʻo A a me B, a laila:
P(A B) = P(A) + P(B)
Nā Hanana Kūʻokoʻa like ʻole
ʻO nā hanana kūʻokoʻa like ʻole, ʻo ia nā hanana kahi i ʻole ai ka hanana ʻana o kekahi hanana e pili i ka hiki ke hanana ʻia o kekahi hanana. ʻO kahi laʻana maʻalahi o nā hanana kūʻokoʻa like ʻole, ʻo ia ka hoʻolei ʻana i ʻelua mau ʻāpana kālā i ka manawa like. ʻAʻole e pili ka hopena o kekahi ʻāpana kālā i ka hopena o kekahi.
No nā hanana kūʻokoʻa, ʻo ka hiki ke hui pū ʻia o nā hanana ʻelua ka huahana o nā hiki o kēlā me kēia hanana. Ma ke ʻano makemakika, inā he mau hanana kūʻokoʻa ʻo A a me B, a laila:
P(A B) = P(A) manawa P(B)
Ke helu nei i ka hiki ke loaʻa nā hanana hui
Ma hope o ka hoʻomaopopo ʻana i ke kumumanaʻo kumu o nā hanana hui, i kēia manawa e kūkākūkā mākou pehea e helu ai i ka hiki ke loaʻa nā hanana hui mai nā ʻano hanana like ʻole.
Ka Pahiki o nā Hanana Kūʻokoʻa like
No nā hanana kūʻokoʻa like ʻole, e like me ka mea i ʻōlelo ʻia ma mua, hiki ke helu ʻia ka hiki ke hui pū ʻia ma ka hoʻohui ʻana i nā hiki o kēlā me kēia hanana. No ka laʻana, inā loaʻa iā mākou ʻelua mau hanana kūʻokoʻa like ʻole ʻo A a me B me nā hiki \( P(A) = 0.3 \) a me \( P(B) = 0.4 \), a laila ʻo ka hiki ke hana ʻia kekahi o kēia mau hanana:
P(A B) = P(A) + P(B) = 0.3 + 0.4 = 0.7
Ka Pahiki o nā Hanana Kūʻokoʻa
No nā hanana kūʻokoʻa, hoʻohana mākou i ke kānāwai hoʻonui. No ka laʻana, inā loaʻa iā mākou ʻelua mau hanana kūʻokoʻa A a me B me nā hiki \( P(A) = 0.5 \) a me \( P(B) = 0.2 \), a laila ʻo ka hiki ke hana ʻia kēia mau hanana ʻelua i ka manawa like:
P(A B) = P(A) manawa P(B) = 0.5 manawa 0.2 = 0.1
ʻAʻole kūʻokoʻa kekahi i kekahi nā hanana a ʻaʻole kūʻokoʻa kekahi i kekahi
I nā hihia kahi ʻaʻole kūʻokoʻa a kūʻokoʻa paha nā hanana, lilo ka helu ʻana i ka hiki ke lilo i mea paʻakikī iki. Pono mākou e hoʻohana:
P(A \cup B) = P(A) + P(B) – P(A \cap B) \]
A inā pono, pono paha mākou e ʻike pehea e helu ai iā \( P(A \cap B) \) inā ʻaʻole lākou manuahi me kekahi ʻike hou aku.
Hoʻopili ʻana o ka Probabilitas o nā Hanana Hui Pū ʻia
Ke Ao o ke Kālā a me ka Hoʻopukapuka Waiwai
I ke kālā a me ka hoʻopukapuka kālā, hoʻohana nui ʻia ke kumumanaʻo o ka hiki ke hui pū ʻia e ana a hoʻokele i ka pilikia. No ka laʻana, hoʻohana nā loiloi kālā i ka hiki ke kuhi i ka likelika o nā hopena hoʻopukapuka kālā like ʻole a e hana i nā waihona kūpono. Hiki iā lākou ke hoʻohana i nā hiʻohiʻona hiki ke hoʻoholo i ka likelika o nā pohō ma lalo o nā hiʻohiʻona mākeke like ʻole.
Nā ʻEpekema Kaiapili a me nā Heluhelu
I loko o nā ʻepekema pili kanaka, hoʻohana ʻia ka probability e hoʻomaopopo i nā hanana pili kanaka paʻakikī. No ka laʻana, makemake paha kahi mea noiʻi i ka pilina ma waena o ka hoʻonaʻauao a me ka loaʻa kālā. I kēia hihia, hoʻohana paha lākou i nā hanana hui e kālailai i ka ʻikepili anamanaʻo a huki i nā manaʻo e pili ana i ka probability o hoʻokahi hanana (e.g., loaʻa kahi loaʻa kālā kiʻekiʻe) e hana ʻia ma muli o kekahi hanana ʻē aʻe (e.g., loaʻa kahi kekelē hoʻonaʻauao).
Nā ʻEpekema Kūlohelohe a me ka ʻenekinia
I ka ʻepekema a me ke ʻenekinia, hoʻohana ʻia ka probability e hoʻolālā i nā hoʻokolohua a wehewehe i nā hopena hoʻokolohua. No ka laʻana, i ka physics, makemake paha nā kānaka ʻepekema e ʻike i ka probability o kahi hopena kemika kikoʻī e hana ʻia ma lalo o kekahi mau kūlana. I ka ʻenekinia, hoʻohana paha nā ʻenekinia i ka probability e helu i ka hilinaʻi o ka ʻōnaehana a hoʻolālā i nā huahana paʻa.
Haʻawina Hihia: Nā Pāʻani Kāleka
E lawe kākou i kahi laʻana maʻalahi mai ke ao o nā pāʻani kāleka e hoʻomaopopo maikaʻi i ka hoʻopili ʻana o ke kumumanaʻo o nā hanana hui. Manaʻo mākou he papa kāleka maʻamau o 52 mau kāleka a makemake mākou e helu i ka hiki ke kaha kiʻi i kahi Ace a i ʻole King.
Aia he 4 Aces a me 4 King i loko o kahi papa kāleka. ʻO nā hanana o ke kaha kiʻi ʻana i kahi Ace (A) a me nā hanana o ke kaha kiʻi ʻana i kahi King (B) ua kūʻokoʻa kekahi i kekahi no ka mea ʻaʻole hiki iā mākou ke kaha kiʻi i nā kāleka ʻelua i ka manawa like. No laila, ʻo ka likelike hui o kēia mau hanana ʻelua:
\[ P(A \cup B) = P(A) + P(B) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13} \approx 0.1538 \]
No laila, ʻo ko mākou manawa kūpono e huki ai i kahi Ace a i ʻole King mai kahi papa kāleka ma kahi o 15.38%.
Ka hopena
He manaʻo pono loa ka hiki ke loaʻa nā hanana he nui a he nui nā noi ma nā ʻano like ʻole. ʻO ka hoʻomaopopo ʻana i ke ʻano o ka helu ʻana i ka hiki ke loaʻa nā hanana he nui e hiki ke kōkua iā mākou e hana i nā hoʻoholo maikaʻi aʻe a hoʻomaopopo i ke ao a puni mākou ma ke ʻano waiwai. Inā paha ma ke kālā, ʻepekema pilikanaka, a i ʻole ka ʻepekema, ʻo ka hiki ke loaʻa ka puʻuwai o ka nānā pono ʻana a me ka hoʻoholo ʻana. Ma ka hoʻomaopopo ʻana a me ka hoʻopili ʻana i ka hiki ke loaʻa nā hanana he nui, hiki iā mākou ke luʻu hohonu i loko o ka ʻikepili a hana i nā wānana a me nā hoʻoholo pololei.
