Te Ture Tāpiri i ngā Takahanga e Rua A me B kāore e Tūtahi
He taputapu nui te tāpiri tūponotanga i roto i ngā tatauranga me te ariā tūponotanga. He maha ngā wā ka whakamahia hei whakatau i te tūponotanga honohono o ngā takahanga rerekē e rua, neke atu rānei, e puta ana. I roto i te nuinga o ngā wā, he rerekē ēnei takahanga, arā, kāore e taea te puta i te wā kotahi. Heoi, he maha anō hoki ngā āhuatanga kāore e rerekē ngā takahanga e rua—ka taea te puta i te wā kotahi. Ka matapakihia e tēnei tuhinga te ture mō te tāpiri i ngā takahanga kore-motuhake e rua, arā, a A me B, me te whakarato i ngā tauira tūturu hei āwhina i te mārama ki a rātou.
Kupu Whakataki: Ngā Whakamāramatanga me ngā Ariā Taketake
I mua i te urunga atu ki te ture tāpiri mō ngā huihuinga kore-motuhake e rua, he mea nui kia mārama ki ētahi ariā matua:
1. Tūponotanga: Ko te tūponotanga he ine i te tūponotanga ka puta tētahi huihuinga, ā, ko tōna uara kei waenga i te 0 ki te 1.
2. Takahanga: Ko te takahanga te hua, te raupapa rānei o ngā hua o tētahi whakamātautau matapōkere.
3. Ngā Takahanga Motuhake: Ka kiia he takahanga motuhake ngā takahanga e rua mēnā kāore e taea te puta i te wā kotahi.
Ina kore e tū motuhake ngā takahanga e rua, ko te tikanga he tūponotanga ka puta ngātahi rāua. I tēnei wā, me whai whakaaro tātou ki te taunekeneke i waenganui i ngā takahanga e rua ina tatauhia ana te tūponotanga katoa.
Te Ture Tāpiri i ngā Takahanga Kāore e Tūhonohono ana
I te nuinga o te wā, mō ngā takahanga e rua A me B, ko te ture tāpiri mō te tatau i te tūponotanga o te takahanga A, B rānei koia tēnei:
P(A kapu B) = P(A) + P(B) – P(A kapu B)
Dimana:
– Ko te P(A \cup B) \) te tūponotanga ka puta tetahi o ngā takahanga A, B rānei.
– Ko te tūponotanga o te huihuinga A ko \( P(A) \).
– Ko te tūponotanga o te huihuinga B ko \( P(B) \).
– Ko te P(A \cap B) \) te tūponotanga ka puta ngā takahanga A me B i te wā kotahi.
He aha ai me tango te \( P(A \cap B) \)? Nā te mea ina tāpirihia te \( P(A) \) me te \( P(B) \), ka tatauhia te rohe e tohu ana i te huihuinga \( A \cap B \) kia rua ngā wā (kotahi i roto i te \( P(A) \) me te \( P(B) \) anō). Nō reira, ka tangohia kotahi kia whiwhi ai i te hua tika.
Tauira Konukura
Me tango he tauira tuturu hei whakamāmā ake i te mārama:
Whakaarohia he papa kāri paerewa e 52 ā tātou. Mēnā e hiahia ana tātou ki te tatau i te tūponotanga ko te kāri ka tangohia e tātou he hāpara (takahanga A) he āke rānei (takahanga B), ka taea e tātou te whakamahi i te ture tāpiri kua whakaahuatia i runga ake nei.
1. Te tūponotanga o te tango i tētahi kāri hāpara:
Tekau mā toru ngā hāpara i roto i te kete kāri e 52.
\[ P(A) = \frac{13}{52} \]
2. Te tūponotanga o te tā i tētahi Āce:
E whā ngā Āce kei roto i tētahi kete kāri e 52.
\[ P(B) = \frac{4}{52} \]
3. Te tūponotanga o te tango i tētahi kāri he Āce me he Hēpa (Āce of Spades):
Kotahi anake te Ace of Spades i roto i te kete kāri e 52.
\[ P(A \cap B) = \frac{1}{52} \]
Mā te whakamahi i te ture tāpiri:
P(A kapu B) = P(A) + P(B) – P(A kapu B)
Te tatau:
\[ P(A \cup B) = \frac{13}{52} + \frac{4}{52} – \frac{1}{52} \]
\[ P(A \cup B) = \frac{16}{52} \]
\[ P(A \cup B) = \frac{4}{13} \]
Nō reira, ko te tūponotanga he hāpara, he Āte rānei te kāri i tangohia ko \( \frac{4}{13} \).
Te Hiranga me te Whakamahinga
He whānui te hiranga o te mārama ki te ture tāpiri mō ngā takahanga kore-wehewehe e rua i roto i te tātari raraunga, te tatauranga, me ētahi atu mara pērā i te pakihi, te pūtea, te pūtaiao rorohiko, me te rangahau pāpori. Ko ētahi o ngā tono mahi ko:
1. Tātari Mōrearea: Te tautuhi i ngā huinga pea o ngā momo mōrearea me ngā āhuatanga i roto i te whakahaere mōrearea.
2. Rangahau Mate Urutā: Te tatau i te tūponotanga honohono o ngā momo āhuatanga mōrearea i roto i ngā rangahau hauora.
3. Pakihi me te Pūtea: Te aromatawai i ngā whai wāhitanga o ngā huihuinga maha i roto i te mākete hea, i te taiao pakihi rānei.
4. Te Whakatau Kaupapa Here: Āwhina i te whakatau kaupapa mā te whai whakaaro ki ngā pānga pea o ngā kaupapa here me ngā mahi.
5. Pūtaiao Raraunga me te Ako Mīhini: Whakamahia i roto i ngā tauira matapae e whai whakaaro ana ki ngā āhuatanga maha kāore pea e tū motuhake tetahi ki tetahi.
Whakamārama Whakairoiro
He maha ngā wā, he āwhina ngā whakaaturanga whakairoiro pēnei i ngā tūtohi Venn ki te mārama ki te taunekeneke i waenga i ngā huihuinga e rua. E whakaatu ana ēnei tūtohi i te taunekeneke a ngā huinga (ngā huihuinga) e rua me te wāhi e taupatupatu ai.
Ki te hoki tātou ki te tauira o te kete kāri, ko te rohe taupatupatu i roto i te tūtohi Venn e tohu ana i te Ace of Spades, e taea ai te whakaatu mārama ake i te take me tango e tātou te \( P(A \cap B) \) i te wā e tāpirihia ana te \( P(A) \) me te \( P(B) \).
Whakamutunga
He wāhanga nui o te ariā tūponotanga me ngā tatauranga te ako i te ture tāpiri mō ngā takahanga kore-motuhake e rua. Mā te mārama ki tēnei ariā, ka taea e tātou te tatau tika ake i te tūponotanga honohono o ngā takahanga i roto i ngā āhuatanga tūturu. Kia maumahara tonu, ina kore ngā takahanga e motuhake, me whakarerekē ō rātou tūponotanga honohono kia kore ai e tatau rua i roto i ngā rohe taupatupatu. Ehara i te mea ka āwhina noa tēnei huarahi i te tātari tatauranga engari ka whakapakari anō hoki i te whakatau whakatau e ahu mai ana i ngā raraunga.
E whakaatu ana tēnei tuhinga me pēhea te whakamahi i tēnei ariā i roto i ngā horopaki maha, ā, e whakarato ana hoki i tētahi tūāpapa pakari mō ētahi atu tono i roto i tētahi wāhanga e pā ana ki te tūponotanga me te tatauranga.
