Answering Your Submitted A Level Questions!

for [Music] [Music] [Music] the for okay wait a few more minutes for okay okay so we have two questions to start with um just going to quickly copy them over so uh this is a bit of probability it doesn't look like binomial or or normal distribution or anything like that so piano exam can be taken once or twice those who fail it on the first occasion take it a second time for those making their first attempt 20% pass of Distinction 40 gain an ordinary pass for those making their second attempt the corresponding figures are 10 and 75 so this is of course something called um conditional probability and why is that well because the probability of something happening changes based on a condition so in this case if you fail the first attempt your percentage decreases for the um distinction right it goes from 20% to 10% and your ordinary pass goes from 40% to 75% so it changes depending on if it's your first or second attempt it changes based on a condition so it's conditional probability so the best way to represent conditional probability is definitely through using a tree diagram so realistically I don't actually care about the first attempt but just for the sake of uh consistency first attempt let's put over here what are the three outcomes well you either get a distinction I'm going to call that a uh D an ordinary pass an o or it's a fail okay and I'm just going to write that just to make my life a bit easier then uh for the second attempt again you have a distinction an ordinary and a fail uh in fact let me keep the fs consistent and fail filling in the probabilities distinction for the US is 20% so we can call that 0.2 and ordinary was whoops okay looks like I have to fill that whole thing again perfect of course um let me fill it in again it's 20% for distinction it's 40% for an ordinary pass because the probabilities obviously have to add up to one 0.2 + 0.4 is 0.6 which means 40% also fail same thing for the um second attempt it's 10 and 75 which means it's 0.1 get a distinction 0.75 add those together we get 0.85 which means a 0.15 fail for a second time so part A find the probability that a random candidate chosen will pass the exam with or without distinction now passing the exam well you can either get a Distinction on your first attempt so 0.2 or you get an ordinary pass on your first attempt again because there's only one probability right they've only just done the one attempt I can add them and whenever I say the word or so whenever there's another possibility I add it there is another option though they could fail and get a distinction or fail and get an ordinary pass so plus fail and distinction that means we're timesing them because it's and we have 0.4 * 0.1 and one last one 0.4 sorry it's or and then and times 0.75 shove this all on your calculator and you should get the correct answer so 0.2 + 0.4 + uh 0.4 * 0.1 + 0.4 * 0.75 close bracket we get 47 over 50 which means it's 94 so there is a 94% chance that someone will pass the piano exam Part B A randomly chosen candidate is found to have passed the exam find the probability that this candidate passed with distinction well again um we have this 94 right 0.94 but now we only care about the distinction so randomly chosen candidat is found to have passed the exam there is a 0.94 chance that they pass the exam a distinction would be either 0.2 or it would be a fail followed by a distinction I actually do this in my head that would be 0.24 cool part C two randomly chosen um candidates both take the piano exam find the propy that they both pass one on the first attempt and one on the second attempt so I'm going to put this in big square brackets the two separate people because we're looking for two separate conditions right person one and person two passes but the first one passes on the first attempt well that's fine that's either 0.2 or 0.4 person two fails on their first attempt but then passes on their second and again there's two ways that can happen it's 0.4 time 0.1 or so add 0.4 * 0.75 add those together and we're done so again if you have any questions just let me know probability is all about thinking about the words or and and that's pretty much all it is to add 0.4 uh not and or sorry time another set of brackets 0.4 * 0.1 plus 0.4 * 0.75 51 over 250 there's a 20% chance that's it hope that makes sense the next question that was submitted give you a second to okay for that second question that's in there that is an A2 question so I want to leave that for now candy part only see uh let me think can I actually okay ah I know exactly where you would have gone wrong in this question nitha um because everyone always goes wrong in this question so again we're only looking at part C we're not looking at part um A or B oh interesting okay anyway sorry we're not looking at part A we're just looking at part C so here if I were to draw this diagram out I'm going to draw a big box and I'm going to show you exactly where students go wrong so in the meantime just have a read of this question we're not going to do part A or B because it wasn't requested but the problem comes from the word thrust so you probably get told quite a lot that tension looks like this and that is normally true because tension acts to pull things back together so if I try and stretch my pen try and Pull It outwards the pen acts to stop me equal and opposite forces What's Happening Here well the driver is applying the brakes so when he's stopping if you imagine this so this is moving this person stopping instead of pulling inwards the thrust actually pushes is outwards because it's trying to stop the car from hitting so the actual arrows for the thrust in this case are actually pointing in the other direction they are what's slowing down the car so now I hope that makes a bit more sense we have 200g for the trailer we have 800g for the um car there are horizontal resistances they will probably change given that the resistance to motions are unchanged okay so the thrust and the toe bar are both 100 going in these directions it's going to be decelerating so I'm going to put the deceleration here the resistances are 200 and 400 but there's also some he's applying the brakes so that means the brakes are producing a force of f Newtons find the value of F Well you can actually resolve however you like yeah you can literally resolve in any way you like and you'll get the answer so I'm going to resolve just looking at the car okay so if I just look at the car just like that what do I have well I have FAL ma as usual because I like to take the direction of um acceleration as positive that means I'm going to take to the left as positive so what on my force is going to the left we have F the breaking force the force and we have the 400 from the resistive Force minus 100 because we got that thrust pushing it back forward again equals m 800 * a cool so we have F + 300 equal 800 a perfect now so this was just for the car we need to repeat the process uh we could do the tension that might be a good one to do in order to work out a sorry not the tension the tow truck the what's it called again the trailer that's it God do the same thing but with the trailer FAL ma once more so again just looking at the trailer we have the thrust and the uh resistive Force going backwards so that's too 100 + 100 no forces going forward equal ma = 200 a so that's 300 = 200 a so a is equal to 300 over 200 so equal 3 over 2 which is 1.5 m/s squ then all I need to do is put that into here we have f plus 300 = 800 * 1.5 so now f is equal to 800 * 1.5 subtract 300 so that's 1200 - 300 which is 900 Newtons which makes a fair amount of sense for a breaking force okay okay