35th Wffc Bih 2015

World Fly Fishing Championship 2019

Can you solve the frog riddle? – Derek Abbott

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.

100 thoughts on “Can you solve the frog riddle? – Derek Abbott

  1. I did some thinking
    And eather answer is equally as likely

    More possible combination of possibilities of survival doesn't nessasarly mean your odds are better

    .

    Imagine you had 3 coins & 3 cups
    You place one coin under a cup tails side up, then flip another coin & put that coin under another cup next to that first coin

    Now you flip another coin & put it under the 3rd cup away from the other 2 cups

    Choosing eather the 2 cups or single cup would both give you the same chances of getting heads

  2. This whole problem is flawed, Both 67% and 50% are wrong because you never stated the chance of a male frog croaking.

    Did you assume male frogs always croak?
    Did you assume if the one on the stump is male, it wouldn't croak?
    Did you assume if both on the clearing are male, only 1 of them would croak?

    If you assume none of these things, you should actually go for the stump because that one is 100% female because it didn't croak and on the right, both could be male.
    You're talking about information deleting possibilities even though you didn't provide all the information.

  3. Me:*quickly runs and licks all of them*
    Frogs:*We are all male you were doomed from the start*
    Me:*slowly dies*

  4. I'm confused… if he knew one of the frogs was male, then the probability of the second one being female is 50%
    So there should be a 50% chance either way

  5. The probability of hearing a male croak should be higher when there are two males than when there is just one.

  6. I think this riddle is wrong because there will always be a 50% chance of the frog in the clearing being a female. This is because in 2:50 where you talk about there being a sample space of the frogs, one of them is Frog 1 and one of them is Frog 2, they are not the same. It can’t be expressed in x+y = y+x. When you hear the croak of the male frog it doesn’t just eliminate f-f frogs, it also eliminates either f-m or m-f. Since we eliminate one of the male-female pairs we are left with only two pairs, m-m and f-m (assuming the frog that croaked was Frog 1). We already know that one Frog can’t help us, leaving us with a possible make or a possible female. 1 in 2 chance.
    What would’ve made a difference is if I picked the frog on the stump before hearing the croak. Then I would’ve gotten a 2 in 3 chance of getting a female frog by switching to the clearing. Search up the Monty Hall problem

    I may be wrong but I’m confident that this riddle is.

  7. But aren't there only two options for the clearing? There being two males or one female that's only 2 options 50% chance

  8. I like the concept and your video..
    But i didn't get the probability.. Bcoz.. There is 50% chance both side as we know one of three is definitely male.
    How can we just make a guess about it… It's just the chance right.. We can't use this to determine the whole situation.. I don't know but.. I don't get it… 🤦‍♀🤷‍♀🤷‍♀
    Btw.. I love maths❤..

  9. Love Ted Ed but your logic is skewed on this one. If you are considering that MF is a pair as well as FM being a separate pair, then you must allow this for FF / FF and MM / MM. If the placement next to each other matters, than every set must be doubled, not only the exception of MF placement. With this you have 6 options, but both FF options are eliminated because of the croak. You are left with the possibility of MM, MM, MF, or FM. 50% chance of having a female. You can’t double the set of MF based on frog positioning but not do this same reasoning with the other sets, and thus both options have an equate chance of including a female.

  10. Since there is atleast one male thus the only possibility is of the second one which can be both male or female this the possibility of getting a female in both cases is practically 50%

  11. 67% is the wrong answer
    As we know that there one of them is male so there are only two possibilities
    1- both males
    2-one male and other female
    So probability is just 50% lol🤔

  12. This is wrong. You need to do a few things to fix this; you must define the probability that a single male frog will croak within the period that you observe it. You need to assume that the croaks are all independent events. Call the probability of a single male frog croaking within the observation period P. Using conditional probabilities it follows that the probability of the pair containing 1 female and 1 male is P/(P+P*(1-P)), and the probability of the pair containing 2 males is P*(1-P)/(P+P*(1-P)). The probability of them both being male goes down as P gets large because it's more likely a-priori that you'd hear 2 or more croaks within that time interval rather than 1 croak. To better formulate the problem you need to get rid of the croaking and just come up with something that communicates that at least 1 of the two frogs is male.

  13. I'm almost certain 50% is the correct answer, heres why:
    The lack of knowledge for which frog croaked does not increase your chances of survival. If you had seen which frog croaked, you would know the other one had a 50% chance of being male or female. Missing knowledge does not in reality increase your survival chance.
    The accurate statistics actually need to be split into two realities, equally likely, and averaged together.
    Either the left frog croaked, so you are left with options m/f or m/m for one reality. Or the right frog croaked which leaves you with option f/m or m/m. Since you don't know which reality is true, you average the two 50% realities together to come to a conclusion of 50%.

  14. Oh wow this is the first riddle I got right even though I have been watching these riddles for about a year

  15. @3.11 there will be Either 2 males ..or 1 male and a female …there are only 2 combinations….it doesn't matter with the position of the male and female frogs…so it's 💯% safe to go to 2 frogs side rather than 1 frog side….why are they making it so difficult…this is wrong Ted ed

  16. 2:48 the first one and the last one are practically the exact same… You have 100% the one is male and 50% the ather one is female

  17. There is a 50% chance for either side. For the side with 2 frogs, there are 4 possibilitie:
    The first frog croaked, and the second frog is male (no good)
    The first frog croaked, and the second frog is female (Good)
    The second frog croaked, and the first frog is male (no good)
    The second frog croaked, and the first frog is female (Good)

    TED ED is incorrect in this riddle.

  18. Their Sample Space table at 3:06 misses out the second MM option.

    If they are including MF and FM they need to add it.

  19. For those who keep saying that it is 50%, not 67%, go search for the Monty hall problem. It should explain it in detail

  20. this logic doesn't make sense to me. when you know that one of the frogs in the clearing is a male, that just means that the other has a 50/50 chance of being female, so it doesn't make a difference which way you go.

  21. Somehow you know enough about the fauna in this random forest to determine a frog's gender and medicinal properties and you possess the ability to mathematically calculate the odds of your survival but you don't know that you shouldn't eat random mushrooms from the forest?

  22. To all the people saying that it’s 50% on both sides just think of it as flipping 2 coins you’re more likely to get 1 head and 1 tails than getting the same side to show up for both coins. Seriously this is like statistics lesson 1.

  23. I went for the two frogs because of the logic that a male's call is likely meant to attract a female. Additionally, I know that with toads (and also frogs, I assume) that if you put a bit of pressure on the back of the neck by gently pinching in just the right place, they'll start croaking if they're male.

    The pinching trick works because it simulates another male grappling on to mount a supposed female. A male getting gripped this way will start croaking to say "Hey, I'm a dude. Get off and get a lady."

  24. Incorrect, it's 50% both ways. You know that the choice with two frogs has a male, which is not useful to you, so you can ignore it. That leaves you with one potential female frog on each side and there is a 50% chance of either frog being female.

  25. Looking at reply chains here, this riddle appears to be one of if not THE most argued riddle in Ted Ed's library. In the end, I don't really know how to say I'm on either side without starting a huge argument in the replies, so I'm not gonna bother continuing an argument, we may keep our opinions in peace while we say what those are and explain our reasoning. After seeing this argument, my logic has led me to side with the 50/50 side of things. Please peacefully discuss this in the replies if you want to. (Granted that's even possible anymore…)

  26. your conditional probability on the clearing is right, 67%
    but it cannot be compared to the probability on the stomp, 50%
    because we need to see the problem as a whole, not to compare them while being in different context
    so the right answer is still 50:50

  27. I picked the left one, my first thought was that it was a 50/50 chance but immediately after that I also thought "wait what if both of them croaked??" So that means I have either a male, female pair… male, male pair or female, male pair. The odds are still with me!

  28. This was really easy, after having the Monty Hall problem hammered into my brain in every math class I’ve ever had.

  29. if I flip a coin there is a 50% chance it'll be heads, heads
    if I flip a coin there is now a 25% chance it'll be heads, heads
    even though it's still 2 outcomes there is a 12.5% it'll be one of those 2.

    every flip has a 50-50 chance

  30. You have to go to the log cuz if one of two is female the would be mating instead of calling to the other frog that means the other must be female

  31. If you see it as "how many chances there are to survive " there is no difference between the clearing and the tree (1/2)
    If you see it with probabilities and count Female-Male ,Male-Female as two cases (which is ONE case in reality because you don't care which is the female since you will lick them both) then yes there are more possibilities in the clearing (2/3)

  32. I couldn't find the answer myself but the real answer is that you shouldn't eat that mushroom and start the riddle in the first place!

  33. Flip 1,000 pairs of coins onto the ground. Remove all heads-heads pairs. Cover one coin out of each remaining pair, leaving a tails uncovered. ~67% of the coins you covered are heads.

  34. Honestly i think its wrong that you have a chance of 67 percent to get a female frog. Because one of the two male female pairs includes, that the frog which made the Sound ist female. So the Chance is 50 percent at both sides.

  35. I'm a little confused as to why we have mf and fm in the set
    Just because one is male, it shouldn't cause the chances of the other being female to go up
    The remaining frog has a 50% chance of being male or female
    If you're going to lick both, the equation should be based on inclusion and not order

    They probably wanted to make it like the monty hall problem, and even though I understand that, I am still confused by this

  36. Ted: Give solution
    Me: "With a thinking process that long, I won't even make it to the first sentence he explain"
    "Forget it, frogs won't just sits there and let u lick them, chasing them afterwards will be impossible, how about some goodnight's rest and some food in the backpack? To my biology knowledge the kinds of mushrooms that kills you doesn't come in blue…" Lamo~

  37. This one is incorrect . When you hear the frog croaking it is 100% sure it is male. So you just have 50% possibility for the other one to be female . Your riddle would be correct if you knew for fact that both are not female but didn’t know how many males were there . There is still a slightly better chance since there is one less male to be afraid of but it becomes 50.0001 approximately depending on the number of frogs

  38. Could you interpret this as a variant of the Monty Hall Problem? Basic idea is there are three doors, behind one is a prize, you choose one at random. One swings open and reveals nothing. Do you then switch your door? The answer is yes because you had a 1 in 3 chance of getting your first guess right and so your chance of the switch being right is 2 in 3. The frog on the stump is your initial door and the croaking frog is your revealed door. You therefore always go for the clearing.

  39. He only had time to go in one direction and he totally wasted it on this riddle. Starting to move is the best option.
    This is just a joke, though. Love to exercise my mind.

  40. We have 2 coins and throw them together. What' the probability of a coin to be "head" provided that we know the other coin is "tail"?! The question looks weird? so does the riddle.
    The conditional probabilities are effective when the two events are dependent, it doesn't apply on the independent events.

  41. I personally think the answer is not 67% nor 50%. Once one of the frogs has been determined as male, the other one actually now has a less than 50% chance of being male because the other male has been removed from the population in which there is a 1:1 ratio of male:female. So my answer is slightly less than 50% chance of survival depending on population size.

  42. Combinations don't care about order. Male-female and female-male is the same thing. You're using permutations in your answer where order matters, and i that's inaccurate in this case

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