Ma ka pāʻani liʻiliʻi ʻo Bowser's Big Blast mai Mario Party 2 a me Mario Party Superstars, koho nā mea pāʻani i hoʻololi hoʻokahi i ka manawa. Hoʻokahi pololei e hoʻoulu i kahi pōkā, palekana nā mea ʻē aʻe. Ke hoʻomaka me \(4\) mea pāʻani aia nā \(5\) hoʻololi. 'O ka mea e kaomi mua, e eo 'o ia i ka \(20\,\%\) ; ʻO ka mea hope loa e kū ana i mua o nā pihi \(2\) wale nō he \(50\,\%\) . Eia nō naʻe, ʻaʻole ʻoi aku ka nui o ka pohō o ka wahi hope. Ua kū mai ka kū'ē'ē ma muli o ka hoʻohālikelike ʻana i nā probabilities ma nā wahi like ʻole o ka manawa.
Manaʻo mākou ua māhele like ka detonator ma waena o nā hoʻololi manuahi a ʻaʻole ʻike ʻia. Loaʻa wale ka manawa o ka mea pāʻani hope inā ua paʻi pono nā mea pāʻani mua \(3\) , ʻo ia hoʻi, ʻaʻole i pahū ka pōkā. 'O ka manawa o kēia 'o \(\frac{4}{5}\cdot\frac{3}{4}\cdot\frac{2}{3}=\frac{2}{5}=40\,\%\) . Ma ke koena \(60\,\%\) e pau ka poepoe mamua. Inā hoʻonui ʻoe i ka manawa o ka loaʻa ʻana o ka huli ma ka pilikia e hiki mai ana, loaʻa iā ʻoe ka like \(20\,\%\) me ka mea pāʻani mua. Loaʻa kēia i ke kūlana hope:
$$\frac45\cdot\frac34\cdot\frac23\cdot\frac12=\frac15=20\,\%.$$
Ma ka \(q\) hōʻike mākou i ka hiki ke hoʻopau ʻia ka mea pāʻani i hāʻawi ʻia, ʻoiai ma hope o kekahi helu o ka hana hou ʻana. I ka pōʻai mua, ʻekolu mau hihia: Me \(1/5\) ua pā ia i kēia mea pāʻani. Me ka \(3/5\) ua pā ia i kekahi o nā mea ʻē aʻe; ʻaʻole e hoʻopau ʻia kā mākou mea pāʻani ma hope. Me \(1/5\) ola nā mea a pau a hoʻihoʻi hou ʻia nā hoʻololi. A laila, ʻaʻole i hoʻololi ʻia ke kūlana, no laila ua hou ka manawa i makemake ʻia \(q\) . ʻO ia ke kumu e pili ai:
$$\begin{aligned}q&=\frac15+\frac15q,\\\frac45q&=\frac15\quad\Longrightarrow\quad q=\frac14.\end{aligned}$$
Ma hope o ka hoʻopau ʻana aʻe, hoʻomaka hou nā mea pāʻani i koe ma nā huaʻōlelo like. ʻO ka manawa e ola ai a hiki i kēlā manawa ʻo ia ka \(3/4\) i ka wā e hoʻomaka ai me \(4\) nā mea pāʻani, a laila me \(3\) nā mea pāʻani \(2/3\) a i ka hope me \(2\) nā mea pāʻani \(1/2\) . Inā hoʻonui ʻoe i kēia mau kūlana kūlana o ke ola, loaʻa iā ʻoe \(25\,\%\) ka manawa e lanakila ai no nā kūlana hoʻomaka mua a hope. Ma keʻano laulā, me nā mea pāʻani \(n\) , lanakila nā mea a pau me \(1/n\) . ʻAʻole kōkua nā kala i ke kumu hoʻohālike. No ka lanakila holoʻokoʻa:
$$P(\text{Sieg})=\frac34\cdot\frac23\cdot\frac12=\frac14=25\,\%.$$
Bowser's Big Blast – Spiel und Wahrscheinlichkeiten von David Vielhuber auf CodePen.