Can you solve the frog riddle? - Derek Abbott

Prevodilac: Marija Kojić Lektor: Jelena Kovačević

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

Dakle, zalutali ste u ogromnoj prašumi i pojeli ste otrovnu pečurku.

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

Da biste spasili život, treba vam protivotrov

koji luči određena vrsta žabe.

Nažalost, samo ženka ove vrste proizvodi protivotrov,

Unfortunately, only the female of the species produces the antidote,

and to make matters worse,

i da sve bude još gore,

the male and female occur in equal numbers and look identical,

mužjak i ženka su zastupljeni u istom broju i izgledaju identično,

with no way for you to tell them apart,

i ne postoji način da ih razlikujete,

except that the male has a distinctive croak.

osim što mužjak ima specifičan kreket.

And it may just be your lucky day.

Danas je možda vaš srećan dan.

To your left, you've spotted a frog on a tree stump,

Sa vaše leve strane, primetili ste žabu na panju,

but before you start running to it,

no, pre nego što potrčite ka njoj,

you're startled by the croak of a male frog

uplaši vas kreket mužjaka ove žabe

coming from a clearing in the opposite direction.

koji dolazi sa proplanka iz drugog pravca.

There, you see two frogs,

Tamo, vidite dve žabe,

but you can't tell which one made the sound.

no, ne možete znati koja je proizvela zvuk.

You feel yourself starting to lose consciousness,

Osećate da počinjete da gubite svest,

and realize you only have time to go in one direction before you collapse.

i shvatate da imate vremena da krenete samo u jednom pravcu

pre nego što kolabirate.

What are your chances of survival if you head for the clearing

Kolike su vaše šanse da preživite ako se uputite ka proplanku

and lick both of the frogs there?

i poližete obe žabe tamo?

What about if you go to the tree stump?

Kolike su vaše šanse ako krenete ka panju?

Which way should you go?

Na koju stranu bi trebalo da idete?

Press pause now to calculate odds yourself.

[Pauzirajte sada da sami izračunate verovatnoće.]

3

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2

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Ako ste izabrali da odete do proplanka,

If you chose to go to the clearing, you're right,

u pravu ste,

but the hard part is correctly calculating your odds.

no, teško je tačno izračunati vaše šanse.

Postoje dva uobičajna načina da netačno rešite ovaj problem.

There are two common incorrect ways of solving this problem.

Wrong answer number one:

Prvi pogrešan odgovor:

Assuming there's a roughly equal number of males and females,

ako pretpostavimo da otprilike postoji jednak broj mužjaka i ženki,

the probability of any one frog being either sex is one in two,

verovatnoća da bilo koja od žaba bude bilo kog pola je jedan prema dva,

which is 0.5, or 50%.

što čini 0,5 ili 50%.

And since all frogs are independent of each other,

Budući da su sve žabe nezavisne jedna od druge,

šanse da bilo koja od njih bude ženka ipak bi bile 50% pri svakom izboru.

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,

Ova logika zapravo jeste tačna za panj,

but not for the clearing.

ali ne i za proplanak.

Wrong answer two:

Drugi pogrešan odgovor:

First, you saw two frogs in the clearing.

prvo, videli ste dve žabe na proplanku.

Now you've learned that at least one of them is male,

Sada znate

da je najmanje jedna od njih mužjak,

but what are the chances that both are?

no koje su šanse da su to obe žabe?

If the probability of each individual frog being male is 0.5,

Ako je verovatnoća

da je svaka pojedinačna žaba mužjak 0,5,

then multiplying the two together will give you 0.25,

kada tu verovatnoću pomnožimo

dobijamo 0,25,

which is one in four, or 25%.

što je jedan prema četiri, ili 25%.

So, you have a 75% chance of getting at least one female

Dakle, imate 75% šanse da naiđete na makar jednu ženku

and receiving the antidote.

i dobijete protivotrov.

So here's the right answer.

Dakle, evo pravog odgovora.

Going for the clearing gives you a two in three chance of survival,

Ako krenete ka proplanku imate šansu dva prema tri da preživite,

or about 67%.

ili oko 67%.

If you're wondering how this could possibly be right,

Ako se pitate

kako ovo uopšte može biti tačno,

it's because of something called conditional probability.

to je zbog nečega što se zove uslovna verovatnoća.

Let's see how it unfolds.

Hajde da vidimo kako ona funkcioniše.

When we first see the two frogs,

Kada prvi put vidimo dve žabe,

there are several possible combinations of male and female.

postoji nekoliko mogućih kombinacija

mužjaka i ženki.

If we write out the full list,

Ako napišemo ceo spisak,

we have what mathematicians call the sample space,

dobijamo ono što matematičari zovu prostorom elementarnih ishoda,

and as we can see,

i kao što možemo da vidimo,

out of the four possible combinations, only one has two males.

od četiri moguće kombinacije, samo jedna ima dva mužjaka.

So why was the answer of 75% wrong?

Zašto je onda 75% pogrešan odgovor?

Because the croak gives us additional information.

Zato što nam je kreket dao dodatnu informaciju.

As soon as we know that one of the frogs is male,

Budući da znamo da je jedna žaba mužjak,

that tells us there can't be a pair of females,

to nam govori da ne možemo dobiti par ženki,

što znači da možemo eliminisati

which means we can eliminate that possibility from the sample space,

tu mogućnost

iz prostora elementarnih ishoda,

što nam ostavlja tri moguće kombinacije.

leaving us with three possible combinations.

Of them, one still has two males,

Od te tri, jedna još uvek nudi dva mužjaka,

giving us our two in three, or 67% chance of getting a female.

što iznosi dva prema tri, ili 67% šanse da dobijemo ženku.

This is how conditional probability works.

Ovako funkcioniše uslovna verovatnoća.

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

Počnete od obimnog prostora elementarnih ishoda

koji uključuje svaku mogućnost.

But every additional piece of information allows you to eliminate possibilities,

No sve dodatne informacije vam dozvoljavaju

da eliminišete mogućnosti,

shrinking the sample space

što umanjuje prostor elementarnih ishoda

and increasing the probability of getting a particular combination.

i povećava verovatnoću da dobijete određenu kombinaciju.

The point is that information affects probability.

Smisao je u tome da informacije utiču na verovatnoću.

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

Uslovna verovatnoća nije samo korisna u apstraktnim matematičkim igrama.

It pops up in the real world, as well.

Pojavljuje se i u stvarnom svetu.

Computers and other devices use conditional probability

Kompjuteri u drugi uređaji koriste uslovnu verovatnoću

to detect likely errors in the strings of 1's and 0's

da otkriju moguće greške u nizovima jedinica i nula

that all our data consists of.

od koji nam se sastoje datoteke.

And in many of our own life decisions,

Kao i u mnogim životnim odlukama,

we use information gained from past experience and our surroundings

koristimo informacije dobijene kroz prošla iskustva i okolinu

to narrow down our choices to the best options

da suzimo izbore na najbolje

so that maybe next time,

tako da možda sledeći put,

we can avoid eating that poisonous mushroom in the first place.

možemo izbeći da uopšte i pojedemo tu otrovnu pečurku.