今日下午去中三學生處，研習概率 (Probability) 一課，說到擲兩粒骰子 (fair dice) 的問題。我教學生畫一個 6 x 6 的表格解題，他想了一想，問：骰子只有六面嗎？我回說是，他便立即從房間拿了一盒奇形怪狀的骰子給我看，類似下圖：
栗子妹望著那些骰子，真是愛不釋手！活了這些年，沒見過這麼別緻的東西呢！不知哪兒有得賣？
~‧~‧~‧~‧~‧~‧~‧~‧~‧~‧~‧~‧~‧~‧~
關於 fair dice 的網頁：
http://www.mathpuzzle.com/Fairdice.htm
http://www.mathsisfun.com/geometry/fair-dice.html
The are 別緻 alright. But are they fair?
回覆刪除[版主回覆02/07/2009 20:45:00]Dear Teach: According to the web pages (see links at the bottom), they can be fair. No?
Yes, they can be. I meant to ask if the ones you saw at your kid's home that you like so much were fair. If there're too many sides, it might be tricky to make it fair because everything must be perfectly balanced.
回覆刪除[版主回覆02/07/2009 21:13:00]Then I'm not sure, Teach. He has a dice with 20 sides ...
Let me ask him to do an experiment and calculate the experimental probability!
An experiment with a 20-sider requires a huge sample size. What not just eyeball it to see if all the sides are close to identical in size, and hold it up to see if the center of mass is indeed in the center.
回覆刪除[版主回覆02/07/2009 21:54:00]Dear Teach: The sides are close to identical, but I'm not sure about the centre of mass. How can you tell if it's really in the centre?
真係幾過癮.
回覆刪除[版主回覆02/08/2009 19:55:00]BS2: 係呀，嗰粒20面的骰仔，好鬼得意
by finding the two points connecting the line of symmetry, holding it and spinning the die to see if it spins smoothly
回覆刪除[版主回覆02/08/2009 19:56:00]I see. Will try it next time.
Thanks, Teacher!
又真係幾靚喎。
回覆刪除[版主回覆02/08/2009 19:56:00]閒兄：攞上手玩真係好唔錯架
這些骰主要是用來玩game用的。 一些遊戲店有售，不知道賣麻雀的店子有沒有(我只知道他們有很多種不同顏色的骰子賣)。
回覆刪除[版主回覆02/08/2009 19:57:00]我猜沒有吧？打麻雀的人，要這種骰子來幹啥？
一個關於概率的問題存在心裏很久也沒有答案，就是：
回覆刪除明明交通燈不是紅就是綠，照計綠燈的概率應是50%，但不知怎的，當你行到交通燈前，它卻永遠都是紅燈(尤其當你正趕時間)。
呢d骰真係好過癮呀！
回覆刪除關於紅綠燈問題，這是個墨菲定理(Murphy's law)的應用。以下提出可能的答案﹕
回覆刪除1. 紅綠燈出現的機會不一定是50/50。因為在很多路口，讓車通行的時間通常多於讓人通行的時間。我試過有支紅綠燈等了兩三分鐘也不轉燈，但你們見過哪支紅綠燈讓人有兩三分鐘通行時間﹖通常都只有十幾秒吧﹖ (又﹕所以區議員會把「延長綠燈兩秒」當成「政績」。)
2. 紅燈和綠燈對人而言，在心理上佔據的時間不同。 紅燈是要「等」的，而綠燈不用等(直接走過就是)。所以在印象中，見到紅燈的時間「總和」一定多於綠燈。