The Easiest Problem Everyone Gets Wrong

here vsauce kevin and i'm about to stretch my wink until it breaks. In fact, I have three of these anti-stress emoji called winkies, only one will survive and you will witness an incredibly simple

problem

that almost

everyone

gets

wrong

and in the end it

gets

to the bottom of one of the most famous probability

problem

s of all time is Time to meet the orange, purple and blue winkies. They have been sentenced to death but only one will be forgiven. The other two are walking the green mile but they don't know which two they will be. All they know is that I, Warden Kevin, have to decide right now.

The probability of survival of each winky is one in three, so one over three plus one over three plus one over three equals one and each winky has the same chance of living, there is no paradox here, but the fairest way and less biased of choosing which winky lives is to put three strips of paper in a hat and draw a random color and mix them around your strips and here we go, but what if they know I drew a color? However, I won't tell you which one it is, these winkies would wonder who will live, who will die, and what their personal chances of survival really are. kevin kevin kevin can you tell me I can keep a secret tell me who will live my wink is talking to me and I think I recognize that voice a keeper of internet history how did you end up on death row?

Anyway, I can't tell you who survives. It's just not fair and I definitely can't tell you that. If you live or die I understand that you carry a heavy burden just tell me one of the winkies who will be executed if the purple one lives tell me the blue one if the blue lives tell me the purple one and if I'm going to live just choose which of the other two you would like to name do this for me kevin please i don't know i don't know orange winky really doesn't seem fair please given pretty please you're so handsome and those glasses look so good on you okay, what's the harm?

I can't give Orange Winky any useful information here, okay, Blue will be executed right now. I didn't mean to turn his body upside down like that, but you know what warden Kevin is, huh, he's a cruel warden, Kevin, you fool. I know my odds are 50 50. I will live or the purple one will live. There is no alternative, stupid and stupid. Oh he's so dumb and also fat, oh no he's right. He tricked me with a wink. Now there are only two options, one will live and one will live. He won't, so his odds improved from one in three to fifty fifty right

wrong

Orange Winky, you still only have a one in three chance of living and purple Winky is actually twice as likely to win a pardon.

This may remind you of Monty Hall. problem and we'll see why that's important later, but for now let's look at the only possible scenarios Orange Winky faced. Remember that I can't tell Orange Winky if he lives or dies. When I named Blue, we can compare the two possible outcomes. after naming blue, scenario one where I name blue and purple lives has a one in three chance of occurring. Scenario three where I name blue and orange lives has a probability of occurring of one in six, since one in three is twice as high as one in six and since they are the only two possible outcomes after naming blue, which means that their probabilities have to add up to one, purple actually has a two in three chance of surviving and orange only has a one in three chance of avoiding execution, the probabilities of two events that appear to be equally likely simply are not and we cannot handle that well, it's time to reveal which wiki will live and which wink will die.

This piece of paper determines our surviving and dwelling lives. Sorry Orange Kevin, it's time for you. a we don't have a message turned into a story my body is stretching don't scratch me kevin it wasn't because I called you fat I'm dead welcome to the three prisoners problem which is actually the Bertrand box paradox and a kind of Monty problem Hall, but especially the paradox of the bertrand box that came out the same year that the eiffel tower was inaugurated van gogh painted the night of stories and nintendo kopai began producing playing cards and eventually they made video games in 1889 70 years before recreational mathematics columnist martin gardner began playing mind games with prisoners on his execution date french mathematician joseph bertrand published calculating probability in which he posed a paradox that became the basis for the genesis of monty hall and will force me to put my winkies in the pudding let me explain after making myself a plate of tendees in my favorite sauce My mom secretly hid winkies in these three big candy dishes full of pudding, one of them contains two winkies of the same color, another contains two winkies of a different color and then one contains a winkies of each of those two colors, I'm pretty sure Mom said one winkie color is yellow, but I'm not sure what the other one is.

This is way grosser than I thought it was going to be. Let's reveal the color of this wink. Oh, thank you for licking me clean. Kevin. Your tongue is so soft. Are you alive? You can't kill me Kevin, we're friends now. Okay, clearly, we have an orange wink that somehow came back from the dead and we know that the wink's second color is yellow, but what are the chances of the other wink in this pudding? it's also orange we know that the three plates are orange orange orange yellow and yellow yellow each combination has an equal chance of being chosen at the beginning we also know that this can't be the yellow yellow plate because I just pulled the creepiest orange wink on the planet that means it comes from orange orange or from orange and yellow and both had the same chance of being selected once we draw the orange wink, we know that the odds that the other wink on this plate is orange is 50 50 because we have clearly chosen orange-orange pudding or orange-yellow pudding.

Right wrong again for the same mathematical reason as our prisoner problem. This is the mathematical basis of all these scenarios. Our inability to recognize that what appears to be 50, 50 is actually not. Before we explain any further, let's find out real quick where the winkies are because I don't actually know, this was orange orange, ah, so it was orange, orange jar number two, I can't even tell, yeah, okay, now it's yellow , this one is orange. or is this the yellow jar yellow it's time to find out it looks orange it looks orange let's see yes, there is the other orange so that was our yellow orange, which means this has to be the yellow yellow yellow yellow I already have to clean this pudding or else We can't continue with the video so I'll come back right now the vsauce mukbang part of our video is complete let's get to the root of this problem.

Bertrand conceived his original paradox with gold and silver coins in boxes he had. In the same basic setup we use gold gold gold silver and silver silver with the player reaching into a random box pulling out a gold coin and wondering about the odds of that box containing another gold coin once we draw a gold coin or an orange wink or one of the prisoners to be executed, it seems like our odds of what comes next are an equal 50 to 50. We're just choosing between two leftover options that seem equally likely. We know the other coin is gold or silver, but see if you can pull one out. gold coin, or you take out a gold coin, a gold coin, two or three, and at this point conceptually you know that you are not dealing with the box with the two silver coins, you don't know exactly what it is, but you do know what it's not.

If you choose gold, the other coin is gold two, if you choose gold two, the other coin is gold 1. If you choose gold 3, you will get a silver one, so 2 out of every 3 times you draw gold, it will be combined with another. gold and only one in 3 times will you be stuck with silver, but it's almost impossible to get rid of the notion of two equivalent options, even when the math shows us it's wrong, it's the same reason the Monty Hall problem is a problem, the prisoner's problem. and monty hall add a story to the math and an extra third, it seems like that would make it more complex, but it actually helps you understand probability more easily.

Adding a second player's perspective allows us to see that the guardian will never reveal who lives and Monty Hall will never reveal the door with the money, despite that additional information we are still wrong, why is it so difficult when the solution is right? in front of our face, probably because it's right in front of our face and that's why it's very, very smart? People often get it wrong more than right. I mentioned this in my What's a Paradox video, but when Marilyn Vos Savant wrote in Parade magazine that switching doors in the Monty Hall problem resulted in a two out of three chance of success instead of an obvious 50. 50 trade parade received over 10,000 letters telling her she was wrong, about 1,000 of them were signed by doctors and she claims many were sent on official letterhead from university math and science departments and I still get comments on my video from people at

everyone

.

The world tells me I'm wrong Massimo Piatelli Paul Marini author of Inevitable Illusions said that no other statistical puzzle comes close to fooling all the people all the time and research conducted in 1995 by Granzberg and Brown found that only 13 of the people changed correctly Monty Hall. doors in a 2003 article in the journal of experimental psychology stephan krauss and xt wang described these particular problems from bertrand's box to monty hall as a cognitive illusion claiming that they demonstrate people's resilient deficiency in dealing with uncertainty and found that only three percent in the control group solved the problem with mathematically correct reasoning and that a major problem was perspective when participants were able to think about the problem from Monty Hall's perspective rather than that of the game show contestant. or think like Warden Kevin instead of the orange prisoner winking at his possibilities. choosing the right path improved by moving from simple non-Bayesian thinking to more complex Bayesian analysis.

In the 1990s it seemed there was no way to break the mathematical illusion of the Bertrand box, the three prisoners or the Monty Hall problem that explained mathematics. It doesn't seem to work, it turns out that mathematics is not the problem, we are, uncertainty is difficult for us. Changing perspectives is more difficult. You are watching this video because you are an intelligent and curious person and by altering your perspective you not only discard a mathematical illusion that has perplexed us for over a century because you have identified its flaw not only solve it but accept it absorb it understand it and finally you use it to your advantage you know it and I know it I have a lot of pudding to eat and as always, no, thanks for seeing the pudding, I mean, surprise you.