GCSE MATHS: Probability PART 2 Exam Practice LIVE LESSON 9 EDITED

hey guys just before we get into the lesson I just want to let you know that you can catch these Live on YouTube uh every Tuesday from 6 p.m until 7 P.M in the UK time and that means you can be more interactive you can ask your questions and they'll be answered okay so without further Ado let's get into the lesson okay so uh welcome back guys to another one of the tuition lessons so today as promised we're going to go through some of the much harder probability questions that you can come across uh in your exams so the first few are going to be a very similar style so the method is quite similar but because it's very difficult conceptually I decided to get a bunch of them from different years uh so we can do all of them at once okay but then there are basically two major types of question we're going to be doing today and the first one uh looks something like this so we have some red counters and some blue counters in a bag there's a ratio of red to blue so three to one two counters are removed at random and the probability that both are blue is 1 over 20. so work out how many counters are in the bag before any counters were removed now there are two ways to do this okay um one way is by using a probability tree which again some people like doing these questions tend to be five marks by the way just so you're aware so you can use a probability tree or you can work out the probabilities kind of just in your head so at first I'm going to do it via a probability tree just so you can see exactly what's going on but once you're comfortable you're more than welcome to not use the tree so first of all we don't know how many counters there are that's actually what we're going to be working out so the only piece of information they give us is that the ratio of blue to Red is three to one so what that means is that there are three times the number of blue counters as red sorry not as are red okay so in other words red equals three times blue okay so we can we can actually put in a value what happens when we don't know what a number is well we use a variable so if I say that the number of blue counters is equal to X then the number of red counters equals 3x okay which means the total number of counters is going to be 4X 3x plus X now what we're going to do is write out our probability tree and we're going to look for the branch that leads us to two blue counters being taken okay so if we start it off there are two options at the beginning either he picks a red which we don't actually care about because we want two blue counters right but I'm going to include it just for now and then I'll cross it out later so what's the probability of picking a red counter first well when we work out probabilities what we do is we take the number that we're interested in so the three x red counters and divide it by the total so we're going to have 3x over X over 4X and yes you can simplify this to three over four okay which means for blue counters it would be X over 4X again because we're looking for so again I'm going to continue this where he then picks red and blue again however hopefully you can see that this whole top Branch I don't actually care about because we're looking for two blue counters I'm going to include it just for this first question so you can see what's going on okay so if he takes one red counter the number of red counters left over is now 3x minus 1. right and the total number of counters are now 4X minus one okay and therefore the probability of getting blue is going to be X and again the total number has decreased to 4X minus 1. perfect and a welcome Lila as well so now let's go down the bottom path but again if you notice I actually don't need any of the top stuff because I'm looking for both Blues so from now on I'm not going to include the top branch and the reason why I'll do that is because in your exam it's good practice to do as little working out as possible although that sounds weird you don't want to waste time working out this top Branch if you don't need it okay so let's go on to here I haven't given myself too much room let's do red and blue over here as well so I've taken the blue counter then there's still the same number of red counters but I reduce the total by one and with the blue counters I have x minus one over four x minus 1. and that is what our tree looks like okay now they tell me the probability of getting two Blues is one over twenty so if I work that out the probability of getting two Blues well let's look at our tree if you remember from last lesson when we go along the tree we times it so the probability of getting the first blue is X over 4X policy getting the second blue is x minus one over four x minus 1. and we're told that that will equal 1 over 20. okay so give me a second just to kind of process that all okay any questions at all [Music] perfect okay good so now what I'm going to do is I'm going to cancel this down so you can see that we can cross an X off the top and bottom so that makes it 1 over 4 times x minus 1 over 4X minus 1. and we're solving for x so solving this there's a bunch of different ways so you could times both sides by 4 if you wanted to that's one way to do it or you can actually times the fractions together so when you times fractions you times the numerators so the numerator if you times it by one stays as x minus one times the Bottom by four so we have four times four x is 16x and 4 times minus 1 is minus four equals one over twenty now what we do here in order to solve this is what I like to do is cross multiply so what I do is I again there are a few ways to do this when you cross multiply I'm basically timesing both sides by 20 and I'm timesing it by 16x minus 4. so what that means is this left side is just Times by 20. so you have 20 x minus 1 and because I've also Times by 16x minus 4 it gets rid of the denominator and the right hand side so I want you to let me know if that's okay I have skipped a step so if it's not okay please let me know the other side the over 20 goes away so it just leaves me with 16x minus 4 which is Times by 1 so it's 16x minus 4. don't understand okay cool let's go back so if I want to solve this what I'm going to do is I want to get I want to get rid of the fractions right so what I'm going to do first is times everything by 20. okay both sides by 20. that leaves me with 20 x minus 1 over 16x minus 4. okay and the other side 1 over 20 times 20 is just going to be one right so if you Again by the way this question it probably it's on a non-calculator paper this is just for demonstration if you times a fraction by its own denominator so its own bottom number it just comes one okay it cancels out so this is going to equal 20. yeah so Lila is that okay so there's times both sides by 20. cool now if I want to get rid of this other fraction I need to times it by its denominator so 16x minus 4. let's go down a bit also let me know if the um writing's big enough as well uh so yeah that'd be 20 x minus one and hopefully you're okay with the same logic as this since I've times this fraction by its own denominator the denominator goes away okay so for example if I did 2 over 20 times 20 I'm left with just the numerator okay so it's the same thing here and that's going to equal 20. 16x minus 4. oh wait hold on hold on hold on apologies that should equal one my bad so this just equals 1 times 16x minus four so it's just equal to 16x minus four so is that all okay now so again in future you can kind of uh do it all in one step like I did before it's called cross multiplication if you want to look it up it's just when you times the whole thing by both of the denominators it just gets rid of the fractions Okay cool so now if we want to solve this equation I think we're actually pretty good at solving this kind of equation it's just linear so let's expand the brackets we have 20x minus 20. equals 16x minus 4. so gather the X's to one side so I like to get rid of the smallest X so that's 16x in this case and what I'm going to do is I'm going to start again from up here 20x minus 16x is 4X minus 20 equals minus 4. add 20 to both sides 4X equals 16. so then X is equal to 4. however that's not my answer so this is actually where most students lose the last Mark so some so that by the way this is a Grade 9 question okay so this is the thing that's stopping you from getting a grade nine okay up to now is four marks if we look at the question it says how many counters were in the bag so how many were in total okay so the total is 4X so the total is equal to 4 times 4 which is 16. that's your final answer and that'll be the fifth mark see how sneaky that is so most students so some of the top students get to this step and they're done they say cool solved it be really careful of what the question says and again this is literally like a Grade 9 probability question okay uh any questions about that okay perfect so if you're okay with that that's grade nine probability not too shabby so let's do another one so this question is it'll turn up in another year it's the same thing okay but uh the numbers are different okay so just to make sure you're okay with this let's go through it so again we have a very pretty much the same question okay I probably should both take taken of red Okay cool so in this case we have that again blue is equal to X but in this case red is equal to 4X and so the total equals 5x but again look at the last line we're looking for the number of blue counters which is just going to be X so we don't we won't get tricked like in the previous question okay now once again we can draw a probability tree however as you practice this you might notice you don't even need one you can jump straight to this working out here but let's draw the tree again but I'm not going to draw both branches okay so we have let's say that's blue that's red I'm not going to draw anything up there because we're looking for Two Reds okay but probably getting a blue at first is X over 5X and the red is 4X over 5X now if we just follow the bottom path again I don't actually need this one up here right because I don't care about red blue I care about red red so let's just work out red red well the number of Reds has decreased by one so it's four x minus one over five x minus 1. see how quick that diagram was by focusing on just the bits that you need you can save a lot of time okay and we're looking and it tells me the probability that both are red is 22 over 35. so probability of red red well the problems are getting one red is 4X over 5X probably so getting another X is 4X minus 1 over 5x minus one and that equals is it wait 22 over 35 perfect now we do the exact same thing okay so cancel the X's and then we can again either times the fractions away or we can combine them so 4 times the numerator here would give me 4 times 4X is 16x and 4 times minus 1 is minus four five times five x is 25x 5 times minus 1 is minus 5. 22 over 35. okay so believe you me uh these do get a bit trickier as we go along okay I promise but hopefully this is looking a bit familiar so just to save pain I'll do this one step at a time so times both sides by 35 so we have I'm not going to expand it just yet and that will equal 22. then times both sides by the other denominator again you can do this in one step but if you're ever unsure do it in two steps and that would give me 35 x minus 4. was 22 minus five oh good so now we need to expand the brackets so we can do 35 times 16 which would be 560 X minus 140 22 times 25 would be 550 and 22 times 5 would be a minus 110. okay I'll stop for a second uh is that all okay so far so again very similar to the previous question uh the mental maths so um honestly it's practice yeah it's it's practice uh so what I did is so if I do 35 times 16 in my head I'm thinking of 30 times 16 and I'm thinking of 5 times 16. and because I've done Maths for so long and taught it for so long that's fairly quick for me so the way I do this is 16 times 3 it's 48 add a zero so 480. 5 times 16 would be a hundred and sixty well 160 divided by 2 would be 80 add it together gives you 560. and again I I've mentioned my trick for multiplying by five before you times it by 10 and then half it so 16 times 10 is 160 divided by 2 is 80. and again with 16 times 30 I did 16 times 3 which is 48 add a zero honestly it comes with practice I'm a lot older than you and I've done maths pretty much since I was well since I was in primary school so it's just practice okay it's not about smart or intelligent or anything like that all about practice and yeah you pick up tricks as you go along as well so next uh again if we're solving this it's a linear equation uh hopefully that's fairly standard this is the smaller one so I'm going to subtract 550x from both sides 560 minus 550 is 10x minus 140 equals minus 110 so now I want to get rid of the minus 140 so plus 140 so 10x 140 minus 110 is basically what we're doing is 30 so x equals 3 and if you remember the original question actually said find the number of blue counters which is equal to X so the number of blue counters is indeed three so you won't get tricked in this case but you would have been tricked in the previous one potentially is that style of question okay because the next style is going to look very similar but it's actually different okay it will look similar similar method but it's different okay that's all fine good good good good good okay so the next type it kicks up a bit okay so I've mentioned before that they give you unseen marks right 10 of your grade is unseen okay which means 10 of the marks gives you a more difficult situation okay so when they first gave these questions you can see you're solving linear equations right so one year they decided to give you a quadratic equation to solve now that isn't too bad but a lot of students panicked okay but let's go through it I promise you it's not too difficult so five red and Y blue counters in a bag Imogen takes accounts from the bag puts it back into the bag then takes another counter there's a few different things here okay I'm going to show I'll show you how that kind of uh plays out so let's do it probability that the first counter is red and the second is red is one over nine so again if we draw a little diagram that will be blue that would be red I don't care about that then we're going to have again blue and red but I don't care about this so this is actually a bit trickier so if I rewrite this here so red equals five nice and easy blue equals y which means the total is equal to Y Plus 5. okay so if we go along here what's the probability probability of getting a red well there's five Reds and in total there's y plus five counters now she takes it out and then replaces it so the total number of counters and the number of red counters is exactly the same so that is something that's different a lot of the time they don't replace it is that okay so in this case they're not they're replacing the counter so our probability actually stays the same for both times that will okay for you guys I think that's all right perfect good so again it's a bit tricky so I'm not gonna like everyone does this right but in an exam students tend to read quickly and because you would have practiced so much you'll see this question and you'll start to fill in the blanks your brain will do it automatically right have you ever seen that thing on like Instagram or Facebook where they write words but they scramble the middle of the word but you can still read what the word is it's a similar thing your brain's going to fill in what it thinks should be the question so read it really carefully okay because in this case she puts it back into the bag every student that I see that does this for the first time misses that and they start writing y plus four and four here okay so really be careful tells us that property of the first counter exactly so you know exactly what it is but our brains do it automatically we fill in patterns right our brains do that on purpose so it's not really your fault you just have to consciously change it for exams anyway it's good in general but it's not good uh in exams so basically the problems you're getting too red is one over nine this is pretty easy number so probability of red red is equal to uh one over nine and again this was also in a non-calculator paper okay uh I probably shouldn't have written it like that so let's see how we would we would do it so we have five over y plus five and again multiply it same way five over y plus five equals one over nine so let's do the um multiplication five times five is twenty-five now there are two ways I can write this I'm going to write it like this for now but can you see I could have also written that as y plus 5 squared you see it's the same thing I'm sorry if not it's totally fine but those are both the same thing times both sides by nine 225 times 9 is 225 to work that out quickly 10 times 25 IS 250 so all I'm doing is subtracting 25 from it which is 225. for 9 times 25. okay so 225 over y plus 5 and again if you wanted to write this as squared that's totally fine equals 1. cool now I'm going to multiply by the other denominator which is y plus 5y plus 5 or Y plus 5 squared if you're feeling fancy so we get 225 equals y plus five in Brackets y Plus 5. now whenever we have brackets we started to expand the brackets right so let's expand these brackets we have 225 equals y times Y is y squared 5y plus 5y so we get 10y 5 times 5 is 25. okay so solving this is where some students got a bit scared but the thing is it's just a quadratic right you definitely know how to do this all you need to do is make it equal to zero so we're going to minus 225 from both sides so we get y squared Plus 10y whoops minus 200. equals zero so I'm hoping that you can see all I've done is flipped it round is that okay and then all we need to do is solve this so I'm looking for two numbers they need to times to minus 20. both are add to Plus 10 sorry minus 200 sorry so I would say that that would be plus 20 minus 10. so my two brackets are y Plus 20. y minus 10 equals zero so why either let's write it over here y equals minus 20. or y equals 10. there's a problem I have two answers but if I look at the question it says how many blue counters are there can I say that there are either this or this many so as a challenge to you how many counters are in the bag how many blue cancers are in the bag so is y equal to minus 20 or 10 or have we done something wrong and give me a reason if you can uh Evie why'd you say that and Lila perfect well done you're right it's 10. not negative good it's a number of counters right can I have negative 10 counters no Okay so y equals ten and you can actually just write that you don't need a reason but you don't need a reason I'm going to write a reason because it's not negative can't have negative number of counters good so another time you might see something like this is you know they give you a shape and they give you like X plus one as one side and X plus two is the other side and they say the area is equal to something solve it you'll get a positive and negative answer just be aware that you know lengths can't be negative either yeah really well done so again as practice we're going to go through another question which is very similar to it okay so very very similar okay actually was this question okay first was anything you want explained again or perfect so again these are some of the hardest questions by the way and hopefully you can see why they were hard right like if if you saw this question in an exam and you've never done it before it's not easy but hopefully this is uh helping you understand so again we've got one more example question uh again very similar to what we just did X blue counters for red counter so red equals four blue equals X and that means the total is X Plus 4. now here's a question okay have the count has been replaced no it just says they're removed so in other words not replaced so just as a like a general thing if they're like dealing out cards or picking counters or doing anything like this anything that implies that if it doesn't say it's replaced it means it isn't replaced okay so the only time that you can say that it's been replaced is if it literally says the counters or the cards or the coins are replaced okay if not then you can't assume that it is so this question has become slightly trickier um and we're looking for two Blues so again I should leave it Squad up a bit we have a red don't care the blue then another red don't care and another blue so probability of picking a blue will be X over X plus four because there are X blue counters and there are X plus four total counters now how many blue counters are left it'll be x minus one and how many total counters are left to be X plus three because if I have X plus four minus one it'd just be X plus three are we all okay with that good stuff very good stuff okay now it's saying that the probability of both are blue is saying if we both are blue then what we're going to do is have it'll be one over three okay so probability blue blue is going to be X over X plus four times x minus 1 over X plus three that will equal a third okay and then we're doing the exact same thing again it's a bit more painful because we have a slightly strange set I'm using a writing pad so x times x minus 1 will be X minus one over then we have X plus four X three equals a third okay and then doing the exact same thing again we're going to cross multiply and times both sides by 3 . so the top of this will be 3x x minus 1. over X plus four X plus three equals one and now we're just going to Times by the denominator okay that's with um perfect okay so the next step in solving this will be just to expand and then solve the quadratic okay so it shouldn't be too bad so 3x times x 3x squared minus 3x equals x times x is x squared plus 4X plus 3x or E plus seven X and then Plus 12. hopefully that's not too bad so far is everyone okay with that yeah perfect good so to solve this we want to bring all of the x's and bring everything to one side now the easiest thing to do would be to move all of this to the other side because we don't want to have negative x squared okay so if I move all of this over I get 3x squared minus x squared is 2x squared minus 3x minus 7x would be minus 10x minus and then just minus 12. um is that okay or do you want me to go through that a bit more uh slowly good perfect now when you're solving this again it's a non-calculator paper so you have to factorize or you can use the quadratic formula if you're really confident but what I uh one piece of advice I'd give you is if you can divide by something then do it so can you see I can divide all of these by two right and I get x squared minus 5x minus 6 equals zero that's a lot easier to solve than 2x squared minus 10x minus 12 because you know when there's a number in front of x squared you have to do a slightly longer method usually so uh two numbers at times minus six add to minus five that's going to be minus six and one so we have x minus six X plus one equals zero so we have X is equal to six or X is equal to minus one so again in this case uh you guys gave me the right answer before which one are we going to choose we're going to choose x equals six and that's six marks um the reason why it's six marks and the others were five is because this is a quadratic you have to solve they give you an extra mark okay um I think do you have to solve it by factorizing is that what you mean uh a common factor out of the is that is that referring to this step when I divided by two yeah okay um so you don't have to you don't have to right if I solved this expression here right if I solved it I would get the same answer so you don't have to do it I think what your teachers mean by have to is that you should because it's a lot easier if you want we can solve it that way right now and I can show so like you're looking for two numbers at times the minus 24. add to -10 so that'd be minus 12 and 2. so you have 2x squared minus 12x plus 2X minus 12. yeah you can get you get the same thing right so to yeah so you still get the same thing you don't have to do it the only thing that really matters is the answer but it is it is useful to do it um just so you guys know the next question is actually very similar to this one so do you want me to go through another one where it's a quadratic as practice would you rather we move on no okay Okay cool so the next question that we can go on then so again this is the question that's very similar so I won't go through that this question it is very similar but there's two parts right so five marks and then a two Mark part is seven marks in total so it's probably good for us to go through this um and again it's slightly it's slightly different okay so let's go through this one instead I'm actually quite impressed that you are fine with doing the quadratics this is a quadratic but if you read the question it is slightly different right there are n counters in a bag so they give us that the total equals n four of them are red so red equals four so that means that blue equals n minus four okay then Ross takes a counter from the bag does not replace it and takes another one two Blues is one third okay so once again let's do red blue don't care about this red don't care blue suppose it's getting blue originally is n minus four over n and getting a blue after that would be n minus 5 over n minus 1. it's n minus five because we have n minus four minus another one hopefully that will make sense okay so it says show that right and hopefully you can see that that's basically just when we get to this stage of the working out so we're doing the same thing but we're going to stop once we get our equation okay so two Blues is one-third so we have probability of two Blues is n minus four over n multiplied by n minus five over n minus one should give me a third okay now we're going to follow the same process okay um I won't talk through this too much because I think you guys have got it I've got the hang of it but the second you don't understand just stop me and tell me what um stage you're stuck on bear in mind there is a delay in the live stream so I will be slightly further ahead than you but just tell me when it doesn't make sense okay and I won't waste your time we'll go through this relatively quickly the time's over so in a question like this where some students will make mistakes although they're actually quite generous right because what they've done is they've given you the answer right you know you're going to get this the problem is is when students do this algebra since you've done it so much you tend to rush and you make mistakes now that I've said that I'm probably going to make a mistake so for example they try and expand this whole thing at once okay I would leave the three outside the bracket and expand the two inner brackets first so n times N N squared minus four n minus 5n would be minus 9N plus 20 equals N squared minus n then I expand okay so 3n squared minus 27 n plus 60 equals N squared minus n move everything to one side so I'm going to drag this over 3n squared minus N squared is N squared minus 27 n plus n would be minus 26n plus 60 equals zero uh hold on it should be a two in front of there my bad okay and now if we look yeah it's meant to be 2N squared I did spot that thank you for thank you for pointing that out like I said easy to make a mistake right but as long as you can spot them uh it's not too bad um so show that well if you look if I divide everything by two I get exactly what the question wants me to get N squared minus 13 n plus 30 equals zero which is Point that's five marks I don't think it's too bad in terms of a level maths uh live lessons I do them on Thursdays from 6 p.m to 7 P.M so I do already do the live maths lessons so yeah Thursday 6 p.m uh any questions about that I think that I think that part we're completely fine with find the value of n again I think you guys are completely fine with it to be honest but let's just uh go through the motions but again it was a slightly different question so with mechanics I'm actually going to start that soon because we've almost covered all of the pure stuff but it is every Thursday yeah okay but so far we're doing pure we're going to get on to mechanics and then statistics afterwards okay so again two numbers at times to 30 and add to minus 13. so that'd be negative 15 and 2. so you have n equals 15. or n equals minus 2. so that's our value perfect not too bad I should hope so the next question I have is actually basically a similar question is it and study oh you're right 15 minus sorry yeah you're right my bad complete yeah that's embarrassing yeah so instead what you probably want to have is if I add to minus 13 plus 3 so you would have to have it would have to be n minus 3 and is that n minus three and minus 10 yeah well spotted sorry like I said when you've done the algebra a lot sometimes you rush and you make a mistake like I just did thank you for spotting that UV well done yeah so you know illustrating my point of course uh when you've done this quite a lot you tend to rush and you make mistakes stupid mistakes what I should have done and this is how you can check is I should have expanded this bracket again to show that I get this yeah so if I expanded the bracket I would have seen that I didn't get I think that's actually what Evie did so if you expand the bracket you don't get what you had originally so I should have done that that's my fault for being lazy and rushing a bit but in your exam please please every time you factorize make sure you expand it to check it don't do what I did that was um very bad so in this case how do we tell if it's three or ten well you might be tempted to just say the bigger number but let's have a look right I'm going to rewrite my Solutions up here okay yeah you can set it back in to work out how many are read um or into this original equation you can sub it in okay however so that's one way Evie if you sub in n equals three and n equals 10 into here one of them will give you kind of a good solution however if we have a look for the counters are red and the rest are blue so if you look here right or here better can n be less than four if I sub in n equals 3 here 3 minus four is minus one it can't happen okay so it has to be n equals 10. is greater than or equal to 4. is that okay in fact it's not even greater than equal to it's actually just greater than otherwise you get zero uh do you do you guys see how I got that as the answer yeah perfect okay yeah so the next question actually is a basically a copy of it I think you guys are okay with it are you would you guys say you're okay with it I think you guys are so here's the next style of question um it's not in my opinion anyway it's not as tricky as the others however it is something we should go through because we didn't go through it last week okay so you can uh ease up a bit it's not as bad hopefully so the Box you have red blue black green pens pen is taken at random here's the probabilities that would be red or green the probability that the pen will be black three times the probability that the pen will be blue there are 28 green pens in the Box work out the number of black pens okay lots of information but the bits that we're missing is the probability of a blue or black pen so what if we say that the probability of blue is X the probability of black which I'll say is BL is 3x you guys okay with that because the probability that it's black is three times the probability it's blue so blue is X black is 3x now all probabilities add up to one so in theory the probability that it's red 0.42 plus the probability is blue which is X plus the probability is black which is 3x plus the probability it's green 0.14 should equal one so all I need to do is rearrange this this kind of question uh it's mostly in the calculator paper so if they ever give you probabilities as decimals it's going to be a calculator paper question unless the decimals are really really easy like 0.5 and that would be 0.56 equals one so 4X equals 1 minus 0.56 is 0.44 so X should equal 0.11 all okay with that so I didn't use a calculator but I hope you can see where I got that from as soon as you confirm I will go on stuff so 0.11 for blue black is three times that so 0.33 okay so we've used this piece of information and remember what I said they never give you useless information so you're going to be using all of it and again it's a format question so far we have two marks so Mark for creating this equation and a mark forgetting the probabilities okay now it says that there are 28 green pens in the Box we need to work out the total number of black pens in the Box okay this is where things get a bit interesting okay if there are 28 green pens in the Box then zero point the probability of getting green is 0.14 times the total so if I say the total is just equal to the letter t so times t should give me 28. does that make sense so if you take the probability of something and times it by the total things you have you get the number of that thing in this case yeah perfect so in this case if we take the probability of getting a green pen Times by all of the pens we get the number of green pens out good stuff the total number of pens is just equal to 28 over 0.14 so hopefully you can see this is why they tend to give you a give it in the calculator paper though you can work this out in your head so 28 divided by 0.14 gives you 200. okay so there's 200 pens in total so the number of black pens is just going to equal the probability of getting black pen which is 0.33 times 200 which is 66. okay [Music] whoops that was quite bad uh not that 0.33 times 200 is 66. yes well done Lila you can so 0.14 equals uh 28 or 14 is 28 so you work this out in the ratio you split what's left you can do that well played it's very impressive that you know how to do that well done