 Hey guys, it's MJ and in this video, we're gonna be looking at a probability paradox Okay probability paradox. So it's gonna be this new little series where I look at some interesting probability questions and we try to figure them out as we go along So without further ado, let's let's just get straight into it Let's get straight into it again and the first one that I'm gonna be talking about It's called the million dollar box. So you're on a very strange game show Okay, so you're a little game show and there are two boxes placed before you So let's call this one box one and this one's box two Okay, now box one, it's open. It's open and there's a thousand dollars inside So it's a thousand dollars and it's open and it's guaranteed in box two Well, box two is closed. So you're actually not sure what exactly is inside But the game show host tells you that there is either One million US dollars inside All there's nothing at all Now he doesn't give us the probability of whether it's a million or whether it's zero But what he does is he gives us the following choices. Okay, so we've got choice one We've got choice two and we've got choice three Choice one is that we just take box one Choice two is that we just take box two and choice three is that we take box one and Box two so we take both Now immediately your game theory must be kicking in and me saying oh my gosh, this is The best decision, you know, this is the decision we must be doing because remember these boxes They're closed you can't tamper with them $1,000 open in the one and in the other one it's closed nobody can alter it But it's random between there being a million and they're being zero So this one seems like the best decision, but what happens is the game show host He says something rather interesting and this might change your decision He says that he somehow has the psychic ability and He's always been able to determine whether the box two has the million or whether it has the zero So he's been playing this game for a long time and somehow he always knows What the outcome is gonna be and he says in your case? He says that if you choose just box two He says there's gonna be the one million dollars inside If you choose box one and two he says that box two will contain $0 inside So you look at this and you think well this guy If what he's saying is correct, then we should just choose box two because we're gonna get the million but how Worthy or how you know reliable is this guy's information What he says and this may change your decision again is he says that if I'm wrong I Will give a million dollars to a random person in the audience Okay, so now this is interesting so this guy is pretty sure on his decision So if you trust him You should only choose box two But while you go and you think okay, let me go and choose box two You see box one just sitting there and you think to yourself Well, whether the money is inside or not inside box two Nothing can change that the boxes close. There's no way for him to alter it if I just take box two It's either a million or it's zero But by me taking box one It doesn't influence at all the context of box two so now the question comes down is Do you take box one and box two or do you just use box two? So I'm gonna write it out as a little bit of a probability statement But you can see that we don't actually really matter about the probabilities Why this is a bit of a paradox is because someone is giving us information After the event has occurred which could not possibly affect it, you know retrospectively But are we still prepared to risk a million dollars in that sense? So here we go the probability that Box two is equal to one million Given that you choose Box one as well is Equal to zero According to this guy and the probability that box two is equal to the one million Given that you don't choose you choose only box two is equal to one But the probability that box two Equals one million By itself, you know, it's according to this random Random value or this probability value over here, you know think of it as a percentage So the question that I want to ask you guys is Would you choose box one? Or would you choose box one and two? Let me know in the comment section below and It'll be fairly interesting to see which choices you guys Decide upon I think I think there might be a lot of people who Who might choose box one and box two? Sorry box two only no one would no one would only choose box one That's that's that's like the worst thing to do. Sorry box two Or box one and box two. So yeah, let me know in the comment section below Which one you will do and also let me know if you like this style of video Thinking of making a whole bunch of you know random probability Videos like this just for fun to see how they how they do so hit subscribe hit like if you like this They'll just encourage me to to continue making videos like this Anyway, thanks guys so much for watching and I'll see you next week. I'll probably release these once a week So yeah, I'll see you next week for the next question. Thanks. Cheers