[Music] [Applause] okay so in today's video we're gonna have a look at Venn diagrams so grab a piece of paper grab a pen make some notes we'll have a look at a couple of questions here so this first one says and I'm to be honest before we start we need to have just have a look at this little symbol here this just means the universal set it just means all the numbers that are gonna go inside this Venn diagram somewhere in there and in in that it says all the odd numbers less than 30 so it might just give you the list of them as if it doesn't it's probably best just to write them all out and it's quite a lot of odd numbers between 1 and 30 less than 30 so I'm gonna write them all out but you could just go ahead and write them all out 1 3 in fact let's just write them out 1 3 5 7 9 11 13 15 17 19 21 and the rest now these are all the numbers that are gonna go in the Venn diagram and they are only going to go in there once okay there's not gonna be any repeats of these numbers but they are all gonna go in the Venn diagram now it says set a it's got these numbers and set B's got these numbers now if it doesn't label the circles in the Venn diagram just label them yourself so call this a and this one B so have a look now the first thing I want afire is what can go in the cross over the intersection there so we have a looking a and B there is a 5 in both so let's cross off the 5 and let's put that into the Venn diagram and I'm also gonna cross that off my main list up here as well cross that off so we're not going to put it in twice let's have a look there's also 15 in both sets cross that off and we'll put that in the middle as well and then we'll cross that off the main list so these all the numbers we've got left to put in a Venn diagram there's there's none are in a MB anymore so all those numbers are in set a I'm just gonna put them in the a circle so 9 17 21 and 29 we'll cross those all off and cross them off the main list so 9 17 21 and 29 there we go they're gone and then 25 in B as well so we'll put that one in there again crossing off both lists so in terms of the numbers we have left we've got the 1 we've got the 3 and I'm not gonna circle more just gonna start putting me because the others are crossed off we've got 7 11 13 19 23 and 27 there we go and that is our completed Venn diagram now it could be asked any sort of question on probability here but I've put up a little selection in down the bottom it says a number is chosen at random find the probability that is in sets and then we've got three questions to have a look at so I've got two symbols that we need to know here we've got the U which is the Union and there we go the Union I'll talk about in a sec and we've got the N which is the intersection there we go and these little symbols can be replaced with some words if it helps so the U for union I replace with the word or and the end of the intersection I replace with the word and I quite like replacing it with the word and because the middle letter in hand is n it's always tend to remember the intersection there the N is and so let's have a look at the first one is U so we've got a or b so the numbers that are in a or b and it's a probability so I'll write it as a probability in a sec but if we have a look at the numbers are in a or b or we've got the 9 the 17 the twenty one or twenty nine which is in a we've got the 25 which is in B and we've also got the five and the 15 which is in a and B so just because that's in both doesn't mean it's not an A or B so in fact finding the number that there an A or B is all of these numbers within the Venn diagram ok so they are all the numbers within the the Venn diagram then if we count them up there's one two three four five six seven numbers they're gonna get rid of that highlighter there but we've got seven numbers so it's write that down we've got seven numbers in a or b out of a total and again you can count them all from the Venn diagram or from that list I did at the top but all the odd numbers between 1 and 30 there are 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 numbers they go so it's 7 out of 15 so that word Union if you think about that as like the United Kingdom the United Kingdom the Union is the collection of all the countries there and it's the same for the Venn diagram it's the collection of everything within that sort of a land there if you kind of imagine like a country you've got the collection of all the numbers so you got seven over 15 and it's the union of a and B now if we have a look at the next one so B we've got a NB or they aim to section of a and B which again can replace with the word and so the numbers are in a and B well there are only those two numbers that are in both a and B the 5 and the 15 so that there is the intersection the numbers are in a and B and if we write down a probability about that's two numbers out of again 15 numbers there you go so there's our two options there for the Union or the intersection I've also included this extra one here as well for C which is a dash now if there's a dash with a lesser it means not in a so all that little dash means is any of the numbers are not in a now if you have a look at the numbers at a not in a well we've got the 25 which is in B that's not in a I've got all these numbers around the outside that are not in a but none of the other numbers so that we've got the numbers which are just in a the 9 the 17 the 21 to 29 and we've also got the numbers are in a and B the 5 and 15 but they are also in a so we can't have those 1 so we're just looking at the numbers that are in B and then was on the outside so but one number in B and 1 2 3 4 5 6 7 8 numbers they're in green round the outside 8 plus 1 is 9 so there are 9 numbers and not in a and again that's out of 15 writing as a probability all right there we go so that's everything that you could be asked here on a on a Venn diagram we got two circles that something like one wave got three okay so something a little bit different here we've got three circles again with all the same sorts of symbols what we've got a B and C to fill in here and again some probability questions but it says here the universal set here is the even numbers between 1 and 25 so if we write those down we've got 2 4 6 8 10 12 14 it's a bit annoying having to write all of these down but and it's better just to write down these numbers and do this little easy task here than to miss them out and get it wrong just because you can be bothered to write them down so it's definitely worth writing them down let's have a look then so finding what's in different multiple categories to start with it's quite hard to spot but there can see there there's an 8 in all of them so if we cross off the 8 and we'll put 8 in the middle and we going cross off for my main list its have a look at there any others that are in all of them no if we do find one that's in all of them you can obviously go back and sort that out but there's no none of those I can see so have a look in am be in a and B there's a sixteen in both so there's a 16 min a.m. V so let's cross that off and a and B is this one here so 16 let's cross that off the main list having another look there's nothing else it's in a and B so let's have a look at B and C numbers that are in B and C there's a 4 there that's quite a nice one to see so in B and C that's this cross over here so for in the crossover of B and C let's have a look if there are any others 12 20 24 no the only one last one we need to check is are there any there in AMC and there is there's a 20 there you go so there's 29 see so we can put that one in there 20 and ANC right okay there we go just need to cross those numbers off the main list again which I forgot to do so cross off the 20 cross off the 4 and that's all of them there 1 2 3 4 numbers and they're all crossed off ok so left in a is 2 so we've got two left in a let's cross that off we've got six left in be under 10 so 6 and 10 cross that off the main list 6 and 10 and then 12 and 24 to go into C 12 and 24 again cross those off 12 and 24 and then we've just got a few numbers left to get on the outside so we've got 14 up here in the main list 18 and 22 so 14 18 and 20 to go on the outside box there right that's all the numbers put in so again we've got some probabilities so it says find the probability it's an A and B okay you can always write down the language there a and B that's the intersection of a and B so what numbers are in a and B well this can be a little bit tricky here because a and B you might think is let's have a look at this 16 here but you've also got the 8 no yes it's in C but it is actually in a and B just cuz it's in C as well doesn't mean it's not in a and B so we've got two numbers there that are in a and B so as a probability here and so look that's gonna be two numbers Altaf and again just count how many are in that list at the top there so one two three four five six seven eight nine eleven twelve so two out of 12 there you go you don't need to simplify these probabilities it's fine to just Ally from there even though I said apply simplifies to 1/6 we can just leave that as it is so the next one we've got you we've got B you see so it's a look that's B or C there you go so any numbers are in B or C if we have a look let's see what's in B or C we've got all these numbers here they're in C and all these numbers here that are in B so yes some of them are in a but they are the numbers they're in B or C okay it doesn't say it can't be an A but they are the numbers a and B or C so if we count those up there's 1 2 3 4 5 in C and then an additional 1 2 3 there just in be there so 5 plus 3 is 8 so we've got 8 numbers I'm so lucky we go eight numbers again out of 12 and again it doesn't need to simplify ok so just watch out for those when you get you 3 deven diagrams they're just it doesn't say that it can't be an A so those numbers that are in B or C are all those numbers within the B and the C circle and then the final one here we've got C - okay so there we go not in C oh yeah and let's have a look what numbers are not in C so we can't have any of these five numbers basically so numbers are not in C we've got the two the 16 the sixth or ten none of those numbers left in the Venn diagram there cuz they're all in C and then we've got the one two three numbers on the outside so I probability there we go one two three four five six seven numbers out of 12 okay she's probably very very careful with these okay I've got a couple for you to have a go out so I'm gonna open these on screen now okay so there's two questions they're very similar in the way that they look to the two that I've just gone over obviously different numbers in the actual sets but have a go at those fill them all in and then have a look at the probability questions just remember the N is and the u the Union is all and if there's a little - next the letter which means not in that number so anything this and however many numbers are not in a or b or c whichever it is okay so pause the video there have a go we'll get the answers in a sec okay look at the answers then so for this first one let's start betting the numbers in even numbers less than 30 I'll tell you what I'm not going to write them all down because it's a lot of space here but let's just have a look it's quite small let's see if we can get a bit closer okay right so if we have a look at this one then even numbers less than 30 let's label this a and B to start with and let's just write those numbers down so 2 4 6 8 10 let's just start writing them in okay so if we have a look at the numbers in a and B we just need to think which numbers there are going to be in both and let's think we have 4 6 10 16 18 22 no well then are there no numbers in both let's have a look oh there we go there's 16 in both let's cross that off and stick them in the middle then I'm just about gonna be able to fit this in I guys finish off this list 26 28 and what doesn't work or 2 right so um gotta be careful this it does set even numbers less than 30 so that won't include 30 okay what doesn't say up to 30 or including 30 says less than 30 so I'm going to stop at 28 I've got 16 in our intersection so we can cross that off let's get rid of it from the main list and now we just need to put other numbers in this quite a lot here so we've got 4 6 ah there we go 6 is in both let's just get rid of that falls in there 6 is in the middle and there we go that's across 6 off and then on the a circle we have 4 10 18 22 26 28 bit of a squeeze there let's cross those all off for 10 18 minus 22 22 26 and 28 and then we can look at set B so in set B there is an 8 a 12 14 and a 24 the good thing about crossing them all off the list is if you do do double one up here and you forget that it goes in the middle you'll notice you've already crossed it off so it's have a look at eight we're gonna cross it off so 12 14 and 24 at the end there brilliant I saw a Venn diagram filled in and let's just put the other numbers running outside so there's 2 and 20 and is that all of them 2 and 20 it looks like every numbers crossed off this that's all of them there we go so we've got 16 and sick in the intersection we've got one two three four five six numbers in a one two three four numbers in B and T on the outside what's up those up that's 10 11 12 13 14 numbers and it's double check from your list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 numbers there so it all matches up so the probabilities we've got we've got a and B the intersection of a and B so the numbers are n a and B we've got 16 and 6 there so we've got two numbers out of the 14 numbers that we just counted so 2 out of 14 for a and B and then the numbers that are not in B so none of those numbers in be there let's have a look so that is going to be in if we use a different color here it's gonna be 1 2 3 4 5 6 7 8 so 8 numbers again out of 14 that are not in B those numbers are either just in a or on the outside so eight out of 14 so look at the other one there we go right so odd numbers between 1 and 25 in this fair and Venn diagram so odd numbers between 1 and 25 we've got 1 3 5 7 9 11 13 this is going to include 25 as well doesn't say less than 25 so include 25 so we will go to 23 and 25 will be our last number there we go so in a it says 3 5 okay like well we need to find what goes in the middle so it looks like there's a 5 in all of them so to get rid of the 5 and stick that in the middle and let's start crossing these off our main race there we go anymore there in all of them this 15 I can see an A & B it's not 11 in either of them okay now so there's nothing left to go into all of them so an A and B let's have a look in a and B there is not a 3 not a 9 and there's nothing there's nothing that's in a and B no he's got a 9 or 15 and 21 so nothing that goes into the a and B this little cross over here so that's gonna be left empty so we can get rid of that ask could be empty so in B and C let's have a look there is nothing in B and C either there's an 11 and a 23 and B but nothing in there and let's have a look in a and C there is a 15 there we go through an A and C we can put 15 in cross that off sort of our main list so in a we've got 3 9 and 21 which is definitely not in any of the others so 3 9 and 21 cross that off the main list 3 9 21 and B there is 11 in 23 there we go 11 in 23 cross those off the main list and then in C this 7 and 19 so 7 and 19 and again cross those off the main list and what's left over we can stick around the outside so I said put those into the outside what have we got left 1 13 17 and 25 they're gonna go around the outside of this cross those off make sure they're all gone 1 13 17 and 25 brilliant so in our list how many numbers did we have 1 2 3 4 5 6 7 8 9 10 11 12 13 numbers can always write that down 13 numbers before our probabilities and let's count them in the Venn diagram so 1 2 3 4 5 6 7 8 9 10 11 12 13 perfect it's 13 numbers in the Venn diagram match is what we needed so our first probability here we've got a number of chosen at random find the probabilities in a and C so the numbers are in a and C let's have a look at its highlight these we've got the 15 which is an ANC and we've got the 5 which is an ANC there as well so we have two numbers out of the 13 that we've already counted so 2 out of 13 are in a and in C now the next one numbers are in B or C so it doesn't explicitly say just in the crossover not in the intersection but numbers are in B all there in C so we've got 11 23 and five they are in B and we've got 15 7 and 19 that are in C so for count those up we've got 1 2 3 4 5 6 numbers that are in B or in C and again that's gonna be up to 13 all right there we go there's our probabilities okay right that is the end of this video for Venn diagrams then and so hopefully found that useful I'm going to make another video going over some harder Venn diagrams where you've got to actually start thinking about doing a little bit of sums to get your numbers into the Venn diagram so I'll be making that video soon but that there is just a little overview of some of the set there looking at the intersection and the Union and just making sure you put your numbers in carefully but there we go hope you enjoyed that I hope it was useful don't forget to Like comment and subscribe and I'll see you for the next one [Music] [Applause]