# Can you solve the frog riddle? – Derek Abbott

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. 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 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. 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%. 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? 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. 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.

I'm here cuz Xqc told me not to klick this. hehehe

If he knew the antidote to the poison of the mushroom, why did he eat the mushroom?

And what about this solution?

There are two frogs on the left and one of them is a 100% male that means there is one 50% frog.

On the right side there is one 50% frog.

So, in my head from mathematical point of view I think left and right should be 50%.

thats so cool[ took me like 5 mins

Wrong math. This math suggests that flipping a coin is 50/50, but flipping a coin next to one that is heads-up has a higher chance of being tails when it lands.

Edit: It also suggests that if there were 100 frogs and you could lick them all, and knew 99 of them were male, you'd have a 99/100 chance of living.

ComplicaTED – ED

reads thumbnailMe: Uh, I probably can’t but whatever

lmao so yea don't eat random mushroom when u go to a rainforest

But wait. The male and female combination is the same as female male because he said we lick both frogs

Doesn't know the mushroom is poisonous but knows the antidote for it?

XQcOW?

I would be dead when i know the answer 💀

Hi, I know my math and will give you an example that has the same problem behind it just to share my view on the matter of probability. Imagine having one coin, this coin has two sides as any and no one argues that is has a 1/2 chance to land on either side. If we now take two coins with the sides of tail and head you will get the following probabilities.

Head:Tail

Heads:Head

Tail:Head

Tail:Tail

If I now were to ask you what the probability of getting one coin that shows heads, you would answer 75%, sound familiar? Now imagine that you get the same question but before you answer I flip one of the coins and you see that it lands on tails. If you would tell me that just because I started with two coins or that the coin that shows tails made the odds higher for heads to show then I would really take a hard look at you and tell you that it is no different than me just flipping one coin.

If you read all that above then now let me tell you that instead of head:tail on a coin there is two frogs on a stump and heads is female and tails is male. Is the chances still 66% as the video says or is it 50%!?

It is wrong answer. Male frogs make this sounds to call female frogs. So, why does it croack if female is here? Becouse they both are male

If one of the frogs is male it's 50% chance that the other one is female.

U should just kill the frogs and the lick them.

Omg! I got it right!!!!!😁 I may have not done the math…..but I saved my life so…

They can't both be female, so the M/F and F/M possibility are really the same one. You've got a 50/50 chance either way.

Male Female is the same as Female Male, there is 1 male and 1 female.

I learned 1 thing from this riddle

DON’T EAT RANDOM MUSHROOMS

As you head for the clearing, before you could even bend down, they jump away.

This comments section is a freaking flamewar.

So the monty hall problem, but with frogs?

What is the guys propability if hes alergic to frogs

What i dont get is that he know the antitode for the poison mushroom but he dont know the musshroom ending him being poisoned at the first place

This riddle sounds like it's trying to replicate the famous "should you switch" gameshow riddle, but it doesn't work here because there is no knowledgeable actor picking the male frog and it's still possible for both the lone frog and the non croaking frog in the pair to be female.

Knowing where at least one male is just means the likelyhood of either choice having a female is EQUALLY greater, albeit negligiblly, than if there where 2 lone frogs.

Erm… The percent is wrong… Hear me out.

If you lick the 2 frogs at the same time. What's the difference between (male-female VS female-male)? Answer : nothing. Its still one probability. You're in need of only 1 female frog. You dont need a female in a specific order. You just need 1 female. That leaves us with (male-female / female-male ) x (male-male) its 1 / 2. Its 50% percent.

That’s not the logic the male female ratio is for the entire frog population. And it could let’s just say 3 female hiding in a bush and 1 male on the tree and 2 male on the ground. What he is saying doesn’t work in real life.

LICK BOTH. THE MALE ISNT BAD

Well who would have thought that the calculation of ted ed would be wrong because of something called a girl boy paradox

but if u do that in that time it would take u a pretty long time and you'll die cuz u only have e liitle time left

But what if every one of the frogs you see are male

But if you hear a male frog croak in the clearing to the left, then why isn't there a 100% chance that there is a male frog there? If both are female, then you wouldn't have heard the male croak from the left in the first place? Unless there is some delusion from the poison mushroom that makes you unable to be sure if you actually heard the croak from the left? Even so, the wording seems unclear.

@TED-Ed you got this one wrong!

Guess what, he had explained it the correct way in his video itself at 1:23 but named it as incorrect way no 1 xD!

Also many would agree that if he had seen the croaking frog while it croaked then the odds would have been 50-50! So, how come the fact that he didn't get a chance to see it while it croaked increases his odds of survival??Does this mean on his way towards the two frogs he shouldn't look at them at all so that he won't unluckily see a frog croak for another time and decrease his odds of survival? No , this argument is flawed!

Anyway the explanation to why the explanation given in the video is wrong:

The sample space shall contain only two possibilities

1)THE left frog croaked: M(Croaked)M , M(Croaked)F

Or

2)THE right frog croaked: MM(croaked),FM(croaked)!

and each of the two possibilities give the probability of a female being licked as 1/2!

AND they both shouldn't be taken simultaneously as in the video as: MM,MF,FM

which assumes the croaked frog can either be in left or right position after it had croaked while in reality as it has croaked it is a specific frog sitting in a specific place and now by conditional probability the fact that the specific frog can't be in both the positions simultaneously which should split the sample space into two possibilities as mentioned above.And we shall not have MF And FM simultaneously in the sample space!

How to live:pause the video.

So forgive me if I am wrong as its 5:30 A.M. and Im watching these videos because I cant sleep (And I study Calculus with minimal stats), but wouldn't you be safer going to the singular frog? Because you will lick both at the other side, M/F and F/M are essentially the same thus making it 50/50 for both sides. If you only have time to lick 1 frog, you have a 50% chance of surviving on the stump. For the pair, you know one frog is male. That leaves the possibility of M/M, F/M, and M/F. Here you have a 33.3% chance of auto death. Thus there is only a 66.6% chance of having a survivable scenario. However, you then have a 50% chance to pick the correct frog. This leaves a 1 in 3 chance of picking a female frog; this is significantly less than the 50% of the solo frog. 0.66×0.5=0.33>0.5 I have not had a proper statistics class, so forgive me if I made any mistakes. Also, feel free to leave your opinion. I am genuinely curious.

I'm a tough guy, I can bring myself to lick all 3 of them.

If you know 1 of them is Male it doesn't give you 67% chance that the other 1 is female because

1=Male(made noise) & 2=female

1=Female & 2=male(made noise)

1=Male (made noise) & 2=male

But there is still one option left:

1=Male & 2=male made noise

So you have 2male & 2 female so its 50/50. The only right answer of it being the 2 frogs is because normally there are no 2 man close too each other (but I do not know if that's a thing with these frog spicies).

since your death is a binary condition, it is safe to say that a male frog is totally useless in this scenario. Therefore, if you lick two frogs, KNOWING that one is useless, then your sample space of possible outcomes goes down to another 50/50, is the second male or female. while TED ED is mathematically correct, the logistics of the example mean it is false. Both choices have a 50/50 shot at survival

Hmm firstly figure out how do you know if the special frog can cure you? If you know it means you know that the mushroom is poissoned and why do you eat that?

If you saw which frog croaked does the probability go to 50/50 or 1/3

Ted edd please do this again but try to explain it to some of these people a little slower or even try putting it into a real world exaple some of these people really think it's a 50% chance of survival and it's a growing problem

This experiment not only shows that the answer is 2/3 but it's also able to be done in the real world

Try it like this have 2 coins flip them and cover them have someone else look at them ask them if there is at least one head coin if they say no re shuffle because to get an answer you need at least one to be a head if they say yes record weather or not there is also a tails

There is 4 sets that the person looking at the coins will see

HT

HH

TH

TT

But they will only call out the

TH

HH

HT

And tell you to re shuffle the TT

When you look at both of them it's a 2/3 chance 1 will tails

This is just wrong. Because you know one of the fogs croaked, you have to count male – male twice: male who croaked – male who didn't croak and male who didn't croak-male who croaked. So there's 4 different combination which means the left side also has a 50% chance of having a female.

I don't think the orientation of the frogs would make the probability and better. It's still a 50/50 either way you go.

DIeing guy oh no i dont have time to go to both frogs

Lets do a 3 minute calculation about where to go

actually i think u wrong.. .. u put the compination male – female twice ..if u dont mind asking r u thought of that from monty paithon ?

Who else tries to solve the riddles even though you know you can’t

How many are here after seeing presh Talwakar??

hmm….i ate a poisonous mushroom..um…(rumbling inside my bag)ah!here's my antidote!

Eats poisonous shroom

-this trip blows

Licks poisonous frogs instead

Are your teachers busy? Discover: androidcircuitsolver/app.html

Are you sure about this? The 2/3 odds is based on arrangement of the frogs (as in order that they are chosen) rather than combination. The two options that it could be a male and female or female and male are the exact same when it comes to the frogs. We arent choosing a frog out of a hat with a certain number inside. Its completely random

I just dont get how boy and girl and girl and boy can be different. They are both the same exact combination of frogs. Yes there is 4 ways to arrange the facts (bb bg gb gg) but there is only three COMBINATIONS. Boy boy, boy girl, girl girl. The last is not possible so it is either boy boy or boy and a girl. 1/2 someone please give me an explanation if you think you know

When you compare this to a coin situation it makes cents;) so if you flip two coins and your friend tells you that one of them is heads. Then according to this video you would be left with three scenarios. Heads and heads, heads and tails or , tails and heads (no tails and tails because we know one is heads) so that would give us a probability of 2/3 right? No. Because heads and tails, and tails and heads are the exact same thing. Since the order doesnt matter and the only objective is to get one tail, the two options are the same and redundant

Your explanation only makes a shred of sense when you say that you must lick the male frog first. If you dont then your odds are ONE HALF. 50$ to anyone who can explain me wrong. Different names for the frogs doesnt work because it doesnt matter if i lick the girl or boy first

Delete this video

It would be better if they covered up the mistake in this video since a lot of people here to fail to identify the mistake.

Ok where dead now because we did to much thinking

WRONG

you use your running pace and lick all of them

Not using that much math

Bruh bruh bruh

Just go to the clearance and pick up any one frog. It will croak when you touch it. So now you know the answer dummy!

So there is still a 50/50 chance because 1 of 2 is male so 1 is unknown and 1 of 1 is unknown on the other side

the correct answer:

just don't eat the mushroom.

This was a bad one lol

At first I was convinced that there was a mistake in the logic. But for some reason when I treat the frogs as coin flips, understanding gets easier.

but it isn't 67% because the results of 1 being male and 1 being female are the same outcome, so it's still 50%.

or those two frog are trying to mate

but yeah that to

1 male female

2 male male

3 female male

1 and 3 are the same just in different orders (the riddle is not based on order of the frogs, so it doesn't matter which one goes first) so it do be 50/50

I just said 2/3 cause he licked 2 of the 3 frogs.

Male and female is the same as female and male so it is a 50/50 no matter which one u go 4.

Anyone else just wait for the timer to finish when he says pause to find answer because ur too lazy to solve the riddle?

You'll die while thinking up all this

Biggest questions about the riddle… A, why did you not realize the mushroom you were about to eat was poisonous yet you knew the frog would cure it, and B, aren’t most jungle frogs also poisonous?

Can you do standard probability? Ted Ed cannot

This makes no sense to me. Cant you eliminate one frog from the left since it croaked, so its 50 50 either way?

Me:

Runs to the ClearingFrogs:

Jump awayFMLThe answer is wrong, and here is why: it doesn't take the probability of a croak into account. If a croak from a male is rare, than having two males make the sound will approximately doable the probability. So out of the three options, the male option is twice as likely, so the probability of survival are 1/2. If the male frogs are likely to croak, then it's really two thirds. The axact formula is 2/(4-k^2) where k is the probability that you hear a croak

Ok people, stop saying the video is incorrect:

– On the tree stump, there is one frog. 50% chance for it to be male, 50% for it to be female. We all agree with this.

– On the clearing, there are two frogs. IF THERE IS NO MORE INFORMATION AND WE SOLVE THE PUZZLE HERE, there are four scenarios:

1. Male, male (25%)

2. Male, female (25%)

3. Female, male (25%)

4. Female, female (25%)

If you think that 2 and 3 are the same scenario and should be counted as one, imagine this instead: There are two people Alex and Sam. Each day, they can choose to wear a red or blue shirt. That means that there are four scenarios:

1. Alex red, Sam red (25%)

2. Alex red, Sam blue (25%)

3. Alex blue, Sam red (25%)

4. Alex blue, Sam blue (25%)

Yes, 2 and 3 have the same number of red and blue, but those are still different events because the PERSON is different.

NOW, back to the puzzle. The new information that received is: One of them croaked, which means one of them is a male. Do not overthink this: IT DOESN'T MATTER WHICH ONE CROAK, IT DOESN'T MATTER WHICH ONE IS MALE.

ALL WE KNOW IS THAT THERE IS AT LEAST ONE MALE FROG.

The ONLY thing that this tells us is that scenario 4 is now impossible.

To the people who insisted that it matters which frog croaked and listed these scenarios:

1. Male (croaking), male (25%)

2. Male, male (croaking) (25%)

3. Male, female (25%)

4. Female, male (25%)

This is incorrect because you're combining two separate things: The gender of the frog, and which frog croaked.

FIRST you must determine the gender of the frogs:

1. Male, male (33%)

2. Male, female (33%)

3. Female, male (33%)

4. Female, female (0%) [again, you know this because you know there is at least one male]

THEN, you can ask yourself: "If scenario 1 is correct and there are two male frogs, then which one croaked?"

1. Male (croaking), male (50%)

2. Male, male (croaking) (50%)

THEN, you can combine the two things together:

1a. Male (croaking), male (33% x 50% = 16.5%)

1b. Male, male (croaking) (33% x 50% = 16.5%)

2. Male, female (33%)

3. Female, male (33%)

4. Female, female (0%)

Hope this clears anything up, but I highly doubt it because there is nothing more stubborn than a Youtube comment section arguing about statistics (Yes, I know I am a part of that problem now and I recognize the irony)

Plot twist they’re all male

Wrong ans no. Three: "both places have 50% chance because in the pile of two there is only one that we don't know the gender of."

amazingNo it isn't 67% :

https://www.youtube.com/watch?v=go3xtDdsNQM

In my lifetime I have a 67% chance of NOT getting a female.

This wasn’t a riddle.

Does all the calculation

Welp too late hooman

collapses before movingI was losing consciousness still I had 5 minutes to think😑😑

If you bite it and you died, then it's poisonous.

If it bite you and you died, then it's venomous.

I think it will be 50% for both, since male-female and female-male are the same, what we need is the difference.

Why not 1/3? Even if you choose the group with one female(2/3chance )you still have to choose again in that group.

(2/3)*(1/2)=1/3?

yes you only have time to go one way but you have time to solve the riddle

Identity matters. You didnt think at all about identifying left and right as two different chances

Ah Ted-ed. Proving clever people don't know how to apply statistics properly.

They be like * logical

I be like "aight i have chosen death".

I got it right

2:51

Third one down oh heck yeah man. Pronhub will be adding two female frogs next week.

One is still a male, lick both. No need for probability.

It's only the "correct" answer if you interpret the premise this way.

When you know one of the frogs is male, then it doesn't matter there is 2 frogs on the left, because only one of them have a chance (a 50/50 probability, not 2/3) of being a female. So it truly doesn't matt if you go left or right. Because you don't have 3 frogs to choose from. You have 2. The males should not be part of your calculation. They're not relevant to you.

Except that you lick both, and the order in which you lick them makes no difference. All you care about is that one is male and thus may as well not exist, and the other is a mystery. It doesn't matter which one is the mystery frog, only that it's there.

What if

ALLof the frogs were males?Solved: I wouldn't eat a poisonous mushroom.

Him – oh a blue mushroom

Must be OK to eat then