Importance of Natural Resources

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.


Reader Comments

  1. I think the example is a bit off… the math is there, bit the example is off.

    Here is Why.

    We know 2 frogs has these possible combinations.

    mm/mf/fm/ff
    Meaning 3/4 chance of survival.

    We know at least 1 frog is male but not witch one.
    That leaves the following options.

    mm/mf/fm
    Meaning 2/3 chance of survival.

    But if i actually Saw witch frog made the Sound (lets just say the first frog) Then there are only 2 options left.
    mm/mf
    Meaning we are back to 50 % chance.

    In the “real World” it dosn’t really matter if i Saw witch frog made the Sound. Me closing my eyes When i hear a frog Sound dosn’t increase my chances of survival from 1/2 to 2/3.

  2. That is a 50/50 flat chance because u already know that one is a male and the order doesnt matter so u basically have 2 options either u get a male in the second frog that is not a male or u get 2 males n die.

  3. I want to point out that given you know that at least one of the frogs on the left is male, you effectively subtract one frog from the equation on the left, meaning you have equal chances either left or right. saying you have a 2/3 chance is actually completely wrong because it assumes that [male,male] [female,male] and [male,female] all has the same chance which doesn't work because [male,male] and [female,male] has the same chance given that you know at least one is male

  4. Wait, but if you eliminate the factor of the male on one side, that leaves you with one on each side, so you have a fifty percent chance either way

  5. Imagine, You're about to die then you have to take the hardest decision of your life, but you can only solve it with a freaking hard riddle…

  6. It is stated that wether the probability of any frog being either Male or female is independent. Therefore if you have 2 frogs the probability of one being male doesnt affect the probability of the other. In other words P(F) = P(F I M)=0.5. Both sides have the same probability.

  7. I think, that you are wrong. We know 3 things:
    1) there are exact the same amount of f/m frogs. Lets say that there is k male and k female.;
    2) i see exactly 3 frogs now;
    3) on the left there is at least 1 male.

    So, the probability, that on the left side is exactly 1 male and 1 female is (C 1 of K (one male from k – group) times C 1 of k (one female from k- group)) over C 2 of 2k, that give us 2(k*k)/(2k*(2k+1))=k/(2k+1). On the right side a probability of female is C 1 of k over C 1 of 2k-1 so probability is k/(2k-1). K/(2k-1) is larger than k/(2k+1) ->We need to go RIGHT SIDE!

  8. I don’t think this is true. There is a given that one frog is male, there is a 50% chance for the other one. The only justification for the 67% thing is that you don’t know WHICH one is male. This justification is kinda how ppl do the flip two coins question where the probability of one heads one tails is 50% where two heads and two tails are only 25% likely. but in that case, if one flip is given to be heads, the other is a 50/50 chance because it is a completely separate chance, so if one frog is given to be male, it becomes irrelevant and the chances are the same for the clearing and the tree as in both cases, there is one frog that could either be male or female. At least that’s what I think.

  9. You are wrong, the frogs spatial location dosent affect its probability [ i assume you took different probabilities for both sides ]

  10. TED is wrong, the frogs spatial location dosent affect its probability [ i assume you took different probabilities for both sides ]

  11. You are wrong, the frogs spatial location dosent affect its probability, bring those left right frogs together and probability equalizes

  12. You are wrong, the frogs spatial location dosent affect its probability, bring those left right frogs together and probability equalizes

  13. how will that first male frog not increase left frog's chance to be a female ? [ I assume you do spatial probability, in which there is less probability to get more same type frogs in same place ]

  14. how will that first male frog not increase left frog's chance to be a female ? [ I assume you do spatial probability, in which there is less probability to get more same type frogs in same place ]

  15. You’re stranded in a rainforest, and you’ve eaten a poisonous mushroom. To save your life, you need an antidote excreted by a certain species of frog. Unfortunately, only the female frog produces the antidote. The male and female look identical, but the male frog has a distinctive croak. Derek Abbott shows how to use conditional probability to make sure you lick the right frog and get out alive.

  16. They should have not included the croak sound, because now the pile of 1 frogs chance of being a female is 3/3 since it didn’t make a noise, assuming that all males make noise.
    Then the other pile of 2 with 1 boy has 2/4 chance of being a girl.
    If they included that not all males make noise, or that males don’t make noises in the first place then the second pile would again be correct with 2/4 or 1/2 chance of being a female.

  17. This riddle is wrong:
    Male Female
    &
    Female Male
    are the same combination of frogs. In the context of this riddle it doesn't matter which frog is on the right and which one is on the left.
    So there are only 2 possible combinations:
    Female Male
    Or
    Male Male.

  18. Go for the single one. If there are two frogs and one croaked, and the other is female they would already be mating. the frog that croaked was trying to bring the female on the stump to mate with it.

  19. Why don’t we count male female and female male as the same event? I said that one is a male and the other one has a 50% chance of being female. Why does the presence of a male frog change the log situation and make the other one more likely to be female?

  20. 1.Who would think about which frog will you choose? have not many time to think so random or die
    2.you stay there for 4 minute and the frogs run away
    3.who would eat random mushrooms without checking
    4.bring food in forest so you don't starve
    5.frogs live in river so no way you are right

  21. I have a riddle for you: how can the guy actually know the antidote to the poisonous mushroom if he didn’t even know what it looked like?

  22. Since the probability for me is the same in math, then I lick the one in the tree stump because it might be calling out for the frog in the tree stump and because of that, it's most likely possible that the pair are males because it's possible they were still there as a pair before one of them called out for a female.

  23. Shouldn't there be people who check if the math checks out before making these videos? The male/female or female/male option is the same. Order doesn't matter here. l

  24. This riddle is incorrect. Solution:
    The possible combinations in the clearing are 2- Male, Female or Male, Male. So the chances of survival are 50%. At the trunk, the chances of survival are also 50% because the male and female populations are equal so the frog on the trunk could be male or female. Thus, going in any direction gives you a 50% chance of survival.

    P.S The Female, Male and Male, Female combinations are the same: 3:06

  25. This is similar to the Monty Hall problem. I remembered it and applied the same logic to this riddle. Marilyn vos Savant was the one to figure out this puzzle.

  26. Wait…. If you know what the male's croak sounded like, if the one on the stump sounded like a male frog why would you go there knowing it was definitely male? Bruh
    If it didnt sound like a male, you got a 100% chance surviving durh

  27. INCORRECT MATH. This one would be 50% chance both ways you go. For the left side if one of them is male then the other one has a 50% chance male 50% chance female. Then the right way is also 50% male 50% female. So it doesn't matter which way you go.

  28. i was literally just like "the clearing because 2 frogs is a higher probability than 1 frog" i didnt even do anything lmao

  29. MindYourDecisions called you out on your mistake. The problem this riddle was trying to show is the probability given that at least one of the two frogs is male but what it actually showed is the probability given that exactly one of them croaked.

  30. 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%.

  31. 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.

  32. 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%!?

  33. 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

  34. 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

  35. 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.

  36. 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.

  37. 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.

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

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