?Can you solve the frog riddle

你能解決青蛙之謎嗎

來源視頻

So you're stranded in a huge rainforest, and you've eaten a poisonous mushroom.?

To save your life, you need the antidote excreted by a certain species of frog.?

Unfortunately, only the female of the species produces the antidote,?and to make matters worse, the male and female occur in equal numbers and look identical, with no way for you to tell them apart, except that the male has a distinctive croak.

假如你被困在一個巨大的熱帶雨林里，然后你吃了一個毒蘑菇。

想要自救，?你需要由青蛙分泌的一種解藥。

不幸的是，只有雌性青蛙才能分泌這種解藥。然而更糟糕的是，雌雄青蛙數(shù)目一樣且長相一樣。你沒有辦法區(qū)分他們。除了雄性青蛙有不一樣的叫聲。

And it may just be your lucky day.?

To your left, you've spotted a frog on a tree stump, but before you start running to it, you're startled by the croak of a male frog coming from a clearing in the opposite direction.?

There, you see two frogs, but you can't tell which one made the sound.?

You feel yourself starting to lose consciousness, and realize you only have time to go in one direction before you collapse.?

What are your chances of survival if you head for the clearing and lick both of the frogs there?

What about if you go to the tree stump??

Which way should you go?

Press pause now to calculate odds yourself.?

3 2 1

可能只是你運氣好，

在你的左邊，?你看到一只青蛙在樹樁上。但在你沖向它之前，你被一只雄性青蛙的叫聲嚇到了，聲音很明顯來自相反的方向的空地。

在那里有兩只青蛙，但是你并不能分辨是哪一只青蛙叫的。

你感覺到自己開始逐漸失去意識，并且意識到在你暈倒之前你只有足夠的時間往一個放向去。

你的生存幾率是什么呢，如果你去空地然后舔那里的兩只青蛙？

去樹樁的生存幾率又是多少呢？

你應該去哪一邊？

請暫停視頻思考兩個選擇的利與弊。

三二一

If you chose to go to the clearing, you're right, but the hard part is correctly calculating your odds.

There are two common incorrect ways of solving this problem.?

Wrong answer number one: Assuming there's a roughly equal number of males and females, the probability of any one frog being either sex is one in two, which is 0.5, or 50%.?

And since all frogs are independent of each other, the chance of any one of them being female should still be 50% each time you choose.?

This logic actually is correct for the tree stump, but not for the clearing.

如果你選擇去空地，你的選擇是正確的。但是困難的是如何正確的計算幾率。

有兩個常見的不正確的解決辦法

第一個：假設雌雄青蛙數(shù)量大致相同，一只青蛙是雌或是雄的概率是零點五或者百分之五十

因為所有的青蛙都是獨立的個體，在你選擇的時候，任意一只青蛙是雌性的可能性應該仍為百分之五十

對于樹樁部分，這個邏輯其實是正確的但是對于空地來說不是

Wrong answer two: First, you saw two frogs in the clearing.

Now you've learned that at least one of them is male, but what are the chances that both are??

If the probability of each individual frog being male is 0.5, then multiplying the two together will give you 0.25, which is one in four, or 25%.?

So, you have a 75% chance of getting at least one female and receiving the antidote.

So here's the right answer.Going for the clearing gives you a two in three chance of survival, or about 67%.

第二個錯誤答案：首先，你看到空地有兩只青蛙

現(xiàn)在你知道至少其中一只是雄性，但是兩只都是的可能性是多少呢？

如果任意一只青蛙是雄性的幾率是百分之五十，把兩個可能性相乘，得到零點二五。也就是四分之一或百分之二十五。

這么說，百分之七十五的可能性其中一只是雌性青蛙，然后你能獲得解藥。

正確答案是：去空地你能獲得三分之二的生存幾率，百分之六十七

If you're wondering how this could possibly be right, it's because of something called conditional probability.?

Let's see how it unfolds.?

When we first see the two frogs, there are several possible combinations of male and female.

If we write out the full list, we have what mathematicians call the sample space, and as we can see, out of the four possible combinations, only one has two males.?

So why was the answer of 75% wrong?

如果你在想這怎么可能是正確答案，是因為條件可能性

讓我們來看看為什么

當我們一開始看到兩只青蛙的時候，有幾個可能的雌雄組合，

如果我們把所有可能性寫出來，就有數(shù)學家所謂的樣本空間，就像我們看到的一樣，在四個可能性中，只有一個可能性有兩只雄青蛙。

那為什么百分之七十五的答案是錯誤的呢？

Because the croak gives us additional information.?

As soon as we know that one of the frogs is male, that tells us there can't be a pair of females, which means we can eliminate that possibility from the sample space, leaving us with three possible combinations.

Of them, one still has two males, giving us our two in three, or 67% chance of getting a female.

This is how conditional probability works.?

You start off with a large sample space that includes every possibility.

But every additional piece of information allows you to eliminate possibilities, shrinking the sample space and increasing the probability of getting a particular combination.

因為青蛙叫給了我們額外的信息

當我們知道了其中一只是雄性的時候，這就告訴我們這其中不可能有兩只雌性青蛙，也就是說我們可以從樣本空間中刪除那一個可能性。留給我們的是三個可能的組合

其中一個是兩個雄性，所以有雌性青蛙的概率是三分之二或者是百分之六十七

這就是條件概率。

一開始，?你有一個很大的樣本空間，?其中包含每一種可能性。

但是每一則額外的信息可以讓你刪除一些可能性。樣本空間逐漸減小，獲得一個特定的組合幾率則增大。

The point is that information affects probability.?

And conditional probability isn't just the stuff of abstract mathematical games.

It pops up in the real world, as well.

Computers and other devices use conditional probability to detect likely errors in the strings of 1's and 0's that all our data consists of.?

And in many of our own life decisions, we use information gained from past experience and our surroundings to narrow down our choices to the best options so that maybe next time, we can avoid eating that poisonous mushroom in the first place.

要點是：信息會影響可能性。

條件可能性并不只是抽象的數(shù)學游戲

它在現(xiàn)實生活中會出現(xiàn)

電腦和其他的裝置會使用條件可能性在1 和 0 中 來偵測我們數(shù)據(jù)中的潛在錯誤

在我們的日常生活中，我們會利用過去經(jīng)歷和周邊環(huán)境獲得的信息來縮小選擇以獲得最佳選項，所以可能下次，我們可以在最開始的時候避免吃那個有毒的蘑菇。