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  • Mining unobtainium is hard work.

    採集難得素是一件費時費力的事情

  • The rare mineral appears in only 1% of rocks in the mine.

    在礦場裡的岩石堆中只會出現百分之一的稀有礦石

  • But your friend Tricky Joe has something up his sleeve.

    但是你的朋友,狡猾老喬握有一手妙計

  • The unobtainium detector he's been perfecting for months is finally ready.

    他花了數個月,終於將難得素偵測器調整至完美。

  • The device never fails to detect unobtainium if any is present.

    若是難得素出現,這個裝置就一定能偵測到

  • Otherwise, it's still highly reliable,

    除此之外,它的可靠性非常高

  • returning accurate readings 90% of the time.

    可以回傳百分之九十的正確讀數

  • On his first day trying it out in the field,

    當他首次將偵測器應用於實務時

  • the device goes off, and Joe happily places the rock in his cart.

    偵測器響了,於是老喬開心的將那塊岩石放入他的推車中

  • As the two of you head back to camp where the ore can be examined,

    當你們倆出發前往可以檢驗岩石的營地時

  • Joe makes you an offer:

    老喬向你提議

  • he'll sell you the ore for just $200.

    他要用兩百元的價格賣你這塊礦石

  • You know that a piece of unobtanium that size would easily be worth $1000,

    而你知道這個大小的難得素一定可以輕輕鬆鬆賣到一千元

  • but any other minerals would be effectively worthless.

    但是除此之外的礦石都毫無價值

  • Should you make the trade?

    那你應該要跟他交易嗎?

  • Pause here if you want to figure it out for yourself.

    (如果你想要自行尋找解答則在這裡暫停)

  • Answer in: 3

    答案將在三秒後揭曉

  • Answer in: 2

    答案將在兩秒後揭曉

  • Answer in: 1

    答案將在一秒後揭曉

  • Intuitively, it seems like a good deal.

    這個交易直覺上相當划算

  • Since the detector is correct most of the time,

    因為偵測器在大多數時候是準確的

  • shouldn't you be able to trust its reading?

    你有什麼理由不去相信它的反應呢

  • Unfortunately, no.

    可惜的是,錯了

  • Here's why.

    理由是這樣的

  • Imagine the mine has exactly 1,000 pieces of ore.

    想像這個礦場實際上有一千塊礦石

  • An unobtainium rarity of 1%

    而當中只存在著百分之一的難得素

  • means that there are only 10 rocks with the precious mineral inside.

    也就是說只有十塊岩石含有珍貴的礦石

  • All 10 would set off the detector.

    這十塊岩石都會觸發偵測器

  • But what about the other 990 rocks without unobtainium?

    但是其他九百九十塊沒有難得素的岩石呢?

  • Well, 90% of them, 891 rocks, to be exact,

    百分之九十的它們,準確地說,這八百九十一塊的岩石

  • won't set off anything.

    不會觸發偵測器

  • But 10%, or 99 rocks, will set off the detector

    但是,百分之十的它們,或其中九十九塊的岩石,將會觸發偵測器

  • despite not having unobtanium,

    即便它們沒有難得素

  • a result known as a false positive.

    這樣的結果就稱為偽陽性

  • Why does that matter?

    為什麼這樣重要呢?

  • Because it means that all in all,

    因為整體來說

  • 109 rocks will have triggered the detector.

    將會有一百零九塊的岩石會觸發偵測器

  • And Joe's rock could be any one of them,

    而老喬的岩石可能會是其中之一

  • from the 10 that contain the mineral

    從包含稀有礦石的那十塊

  • to the 99 that don't,

    到不包含的那九十九塊岩石

  • which means the chances of it containing unobtainium are 10 out of 109 – about 9%.

    代表一百零九塊岩石中只會有十塊包含有難得素,也就是大概百分之九

  • And paying $200 for a 9% chance of getting $1000 isn't great odds.

    而為了那百分之九之獲得一千元的機率付出兩百元不太合理

  • So why is this result so unexpected,

    那麼,這樣的結果為什麼會難以預料呢

  • and why did Joe's rock seem like such a sure bet?

    又為什麼老喬的石頭看似是穩贏的賭注呢?

  • The key is something called the base rate fallacy.

    關鍵就是基本率謬誤

  • While we're focused on the relatively high accuracy of the detector,

    當我們專注於偵測器的相對高準確度時

  • our intuition makes us forget to account

    我們的直覺使我們忘記

  • for how rare the unobtanium was in the first place.

    將難得素的稀有程度放在第一考量上

  • But because the device's error rate of 10%

    但因為偵測器百分之十的錯誤率

  • is still higher than the mineral's overall occurrence,

    依舊高於稀有礦石的整體出現率

  • any time it goes off is still more likely to be a false positive

    不管什麼時候觸發看起來都會像是偽陽性

  • than a real finding.

    而非實際的發現

  • This problem is an example of conditional probability.

    這個問題就是條件機率的一個範例

  • The answer lies neither in the overall chance of finding unobtainium,

    答案不在發現難得素的整體機會

  • nor the overall chance of receiving a false positive reading.

    也不在接收到偽陽性的整體機會中

  • This kind of background information that we're given before anything happens

    像這樣,我們在任何情況發生前所被給予的背景資訊

  • is known as unconditional, or prior probability.

    被稱為無條件機率,或稱為事前機率

  • What we're looking for, though, is the chance of finding unobtainium

    不過,我們所追尋的是

  • once we know that the device did return a positive reading.

    一旦偵測器會回傳正讀數而找到難得素的機會

  • This is known as the conditional, or posterior probability,

    這就是條件機率,或稱為事後機率

  • determined once the possibilities have been narrowed down through observation.

    是一旦透過觀察機率而縮小機率後所決定的

  • Many people are confused by the false positive paradox

    許多人因偽陽性悖論而困惑

  • because we have a bias for focusing on specific information

    因為我們會有專注於特定資訊上的偏見

  • over the more general,

    而非專注於一般的資訊上

  • especially when immediate decisions come into play.

    特別是發生需要立即做反應的決定時

  • And while in many cases it's better to be safe than sorry,

    而當許多需要安全為上的案例發生時

  • false positives can have real negative consequences.

    偽陽性可以帶來非常不好的後果

  • False positives in medical testing are preferable to false negatives,

    在醫學試驗上,比較偏好偽陽性而非偽陰性

  • but they can still lead to stress or unnecessary treatment.

    惟其依舊可以導致壓力或非必要的治療

  • And false positives in mass surveillance

    而在大規模監控的偽陽性

  • can cause innocent people to be wrongfully arrested, jailed, or worse.

    則可以造成無辜的人被不正當的逮捕、監禁,甚至更糟

  • As for this case, the one thing you can be positive about

    在這個案例裡,你可以確定的是

  • is that Tricky Joe is trying to take you for a ride.

    狡猾老喬試著要騙你囉

Mining unobtainium is hard work.

採集難得素是一件費時費力的事情

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B1 中級 中文 美國腔 TED-Ed 岩石 機率 陽性 整體 專注

你能解決假陽性的謎題嗎?- Alex Gendler (Can you solve the false positive riddle? - Alex Gendler)

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    Evangeline 發佈於 2021 年 01 月 14 日
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