He ʻelua aʻu keiki a he keiki kāne i hānau ʻia ma ka Pōʻalima. He aha nā manawa e loaʻa ai iaʻu he kaikamahine? E hōʻike kākou i nā lā o ka pule me nā helu \(1, 2, … , 7\) na \(1\ =\) Pōʻakahi, \(2 =\) Poalua a pēlā aku. I kēia manawa hiki iā mākou ke wehewehe i ka hanana ʻo "i ka lā \(n\) hānau ʻia kahi keikikāne" ʻo \(B_n\) , a pēlā pū me \(G_n\) .
No ka laʻana, \(B_3\) he keikikāne i hānau ʻia ma ka Pōʻakolu a \(G_1\) ʻo ia hoʻi, ua hānau ʻia ke kaikamahine i ka Pōʻakahi. Ma ka hoʻohana ʻana i kēia notation hiki iā mākou ke kākau i nā hanana e like me: \(B_3G_1\) ʻo ia hoʻi: "ʻO ke keiki mua he keikikāne i ka Pōʻakolu a ʻo ke keiki ʻelua he kaikamahine i hānau ʻia ma ka Pōʻakahi".
E noʻonoʻo kākou ʻaʻole ʻoiaʻiʻo loa ka manaʻo o ka hānau ʻana o kahi keiki i kēlā me kēia lā o ka pule (ʻo ia hoʻi, e like me ke kāne o ke keiki, ʻaʻole ʻoiaʻiʻo loa, akā he manaʻo kūpono e mālama i ka pilikia). Ke alakaʻi nei kēia i nā \(27\) i nā ala like i hiki ke hānau ʻia kaʻu mau keiki ( \(B_4\) ke hōʻike nei i kahi keikikāne i hānau ʻia i ka Pōʻalima):
$$
\begin{matrix}
B_4G_1 & G_1B_4 & B_1B_4 & B_4B_1\\
B_4G_2 & G_2B_4 & B_2B_4 & B_4B_2\\
B_4G_3 & G_3B_4 & B_3B_4 & B_4B_3\\
B_4G_4 & G_4B_4 & B_4B_4 & \\
B_4G_5 & G_5B_4 & B_5B_4 & B_4B_5\\
B_4G_6 & G_4B_4 & B_6B_4 & B_4B_6\\
B_4G_7 & G_7B_4 & B_7B_4 & B_4B_7
\end{matrix}
$$
ʻO ka papa ma luna nei he papa inoa piha o nā ala a pau e hānau ai nā keiki ʻelua inā he keiki kāne i hānau ʻia ma ka Pōʻalima. ʻOiaʻiʻo, ma lalo o kā mākou mau manaʻo, ua like like kēia mau hanana āpau. Aia nā \(27\) i loko o ka \(14\) (ʻo nā kolamu mua ʻelua) kahi kaikamahine. No laila, ʻo ka hiki ke loaʻa iaʻu he kaikamahine \(14/27\approx 51,9\% \neq 50\%\) .