Today we’re going to take a look at a mathematics problem that has embarrassed a number of famous mathematicians. To make sure we don’t suffer the same fate, first we’re going to do a probability experiment.
What you will need:
A friend
PHOTO: MICHAEL KEARNEY, TAIPEI TIMES
Two cutout pictures of goats
A cutout picture of a car
Three “doors,” or any objects that can be used to hide the cutouts
▲You can be the host of the show, and have your friend play the unsuspecting contestant. Here’s the problem:
There are three doors. A car is behind one of the doors, and a goat is behind each of the remaining doors. As the host, I’m going to let you pick one of the doors. But before you open it, I’m going to open another door to reveal a goat. You then get to choose if you want to open the door you originally picked or switch to the other door. Your goal is to open the door with the car behind it (Unless you really like goats!).
First have your friend try the experiment 10 to 20 times without switching doors. Then have him try it another 10 to 20 times, making sure to switch doors each time. Record his ratio of wins to losses when he doesn’t switch doors and his ratio of wins to losses when he does switch doors. Is it to your friend’s advantage to switch doors or to stick with his original choice?
(MICHAEL KEARNEY, STAFF WRITER)
今天我們要來看一個讓很多知名數學家難堪的數學問題。為了確保我們不會陷入同樣的窘境,我們要先做一個機率的實驗。
所需材料︰
一個朋友
兩張山羊圖案剪紙
一張汽車圖案剪紙
三扇「門」,或任何可以隱藏剪紙的物體
▲你可以當這個表演的主持人,然後請朋友當不知情的玩家,問題如下:
這裡有三扇門,其中一扇門背後有一輛車,剩下兩扇門後各藏有一隻山羊。身為主持人,我要讓你挑一扇門,但在你打開之前,我會先打開一扇有山羊的門,然後你可以選擇要開原本選的那扇門,或換開另外那扇門。你要打開後面有車子的門才算成功(除非你真的很喜歡山羊!)。
首先,請你的朋友嘗試十到二十次不換門的實驗。然後再請他試十到二十次,這回每次都要選擇另一扇門。記下他這兩項實驗的成功和失敗比,結果是換門、還是堅持原本的選擇對你朋友比較有利?
(翻譯︰袁星塵)
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