mr where's fiverr in pairs of socks to last a week and they are scattered loose in his drawer that's exactly what i do actually each morning he gets up before light and chooses two socks at random find the probably that he wears a matching pair and then there's a whole bunch of sub-questions so um yeah i don't know if they've been smiling on me or something but this is exactly what i do i i don't know i think i have more than 10 socks but same principle right so let's unpack this let's start with the first one because it's the easiest okay each morning he gets up before that and chooses two socks at random find the probability that he wears a matching pair the first morning okay so i'm going to write this as probability i've got a whole bunch of different ones so i want to describe this in a nice succinct but unique way of a matching pair a match on the first morning this is what i'm interested in okay now let's think about this you've got to be careful about i have to pick two socks right i've got to pick two socks um so there's this is a multi-stage event if you want to think about it that way right i've got to pick the first sock and then i've got to pick the second song does that make sense okay now let's think about that first soft let's think about the first one and i'm just going to write out over here i don't have five colors so i'm going to write them just as on different letters okay so here are my ten socks five pairs right five different colors letters you get the idea now think about that first sock does it matter which sock i pick like do i want a particular sock over any other one no it doesn't matter right so the way i can think about this is b this is all about probability right probability and probability is a fraction probability is always a fraction of something over something what are the two things it's favorable outcomes right favorable outcomes the ones that you want over sample space right okay so being that my sample space clearly clearly that's 10 right but when i asked you like which shock do i want well we don't care which one they're all good at this point in time right so the favorable outcomes is 10 right so the first thing i'm going to write is one now you might think well why are you writing that that's not going to change the answer no it's not but it's meaningful right as you will see capturing all our meaning in the working out that we do is critical it starts off easy but it gets tricky later on so i pick a sock okay let's suppose it's this one right first sock down and then i have to pick another one and i want a match that's what i'm after okay so two things have changed firstly the sample space has changed right i don't have ten socks anymore i have nine right so that's reduced okay but also now that i have one of the stocks in particular the favorable outcomes has also changed right now that i've picked one the second one i only want this one this is the only one i'm interested in yes okay so far so good so the probability of getting a match after that second sock will be one times one over nine there you go okay that's one of them there's a probability not so bad right what's so hard about this question well let's progress now they give you a whole variety of different mornings to make it easier to illustrate i'm just going to think about the next day 24 hours passed and now i'm thinking about getting a match the next day okay now keep in mind this is quite separate to what happened before i'm not thinking about a match the first and second morning i would have written first and second morning here not two matches in a row just forget about what happened the previous day i might have got a match i might not have you're just interested in tuesday okay what's the probability of getting a match now okay now who has an answer that jumps out of them any thoughts one over nine okay one over nine now who how many people agree with that you don't have to provide an explanation i'm just interested in who thinks that's a plausible answer hands up straight i actually want to see okay all right all right put your hands down everyone who didn't put their hands up just now i want you to raise your hand for a second okay now i want you to keep your hand up if the reason you don't think it's one over nine is because you think it's something else do you think it's something else or you know put your hand down if you're just not sure but keep your hand up if you think it's something else it can't be one overnight okay now anyone who's still got their hands up because by the way i have my hand up i think this is weird i think this is very strange my intuition is kicking in and saying really anyone's got a hand up why you put your hands down now but why you guys who did have your hands up why do you think this seems strange why do you disagree he has to wash his socks okay so what difference would that bake so you're okay all right so you're saying this whole scenario this scenario is without replacement now hold on a second before we leave off this who thinks elian is right who who agrees this situation is without replacement okay hands down who thinks it is with replacement so okay here's that so i take it a few of you don't know that's okay look at the question again look at it carefully read it with me it's all in the language is there anything in the question that suggests to you it's going to be with replacement or without i think i think alien's right i think it's without replacement i think the key word is he has five different pairs of socks to last the week which kind of implies by the time he gets to friday he's pulling the last two socks out of the drawer um that replacement i think is correct okay now hold on let's keep pushing on that if it's without replacement why is that a problem why does without replacement suggests to you that this answer has a four in it because you would think by by the next morning just like you know when we looked at the first socket and the second saw the sample space would change right and we looked at this yesterday we looked at the idea of dynamic probability where when one thing depends on the previous thing then the probability changes every time you would think the second morning and the third morning every subsequent time probabilities change right so i agree i agree that something seems suspicious with this okay now the question gives you a clue uh right at the beginning i didn't read this it says this question and the next are best done by retelling the story of the experiment now what happens is you go to the answers okay and you look for this and you find sure enough the night actually is correct and then they give a bit of an explanation now their explanation goes like this they say they follow the advice they say retell the story okay so what they imagine is well um you know how i walked through this i said okay the first morning i pick out this one and then i pick out this one right well let's retell it let's retell it like this okay it's monday morning i have ten socks in the drawer okay but instead of getting out monday socks on monday morning i get out tuesday's socks on monday morning now what has changed and the answer is nothing has changed i'm still going to be able to pick from 10 songs it doesn't matter which one i pick first and then i'm still going to get to pick out one that matches out of the nine remaining okay and so you know the second morning actually and the third and the fourth and the fifth they're all the same it's all the same now that's the answer the textbook provides and it's true it really works okay a knife is the answer unambiguously as well no matter how you interpret the question