 upload earlier today I'm hopeful that'll continue work the only difficulty has been our internet phones at the school have been going on and off all day so that means there's something along here with the network so if not I'll try at home I hope to have this up by seven at the latest I hope I hope if all goes well a math teacher who's even dirtier than me yes there are out there believe it or not he put this t-shirt together for his kids he called it Hollywood meets mathematics they had movie titles number one was radians of a lost Ark number two was permutations of a dangerous mind three was dude where's my conic or was return of the radii five was American pie six was that's fifty first dates in base three for those who know your bases seven was Seinfeld eight was finding numeral anybody know what number nine is movie that came out a couple years ago called the thin red line which is the line what the line Y equals X of course which is what the inverse flips around which you'll start remembering when you start reviewing for your final exam what's that one what Lorentz ET very good when you simplify that you'll find that ET I'm quite impressed out of nowhere I'm impressed my friend what's this one the TV show that was on might have been I think it was still on when you were young kids it had two famous twins had two twins on it that have now made their own little children's huh that is the combinatorics for a full house from 13 suits choose one from three of those four of those cards choose three so this is from Brad Epps students in Kamloops number nine is the thin red line and number 11 is full house anyways there's your humor now back to real life let's do some math all right basic rules of thumb I would give you read the questions very very very carefully I'm gonna tell you right now there are questions card questions where I say not just red card not just black card but red face card or black face card or red ace or black ace and for some reason I find kids just missed that last word they see the word red or they see the word black this was Eric Bings only mistake when he was taking math 12 was a great 11 student on this test he read a question wrong he just saw the first word and didn't see the two words describing the cards and was mortified to find that he'd read the question wrong so read the questions carefully okay second hint I would give you is ask yourself how many events are there if there's more than two probably you don't want to do a tree probably you want to do some kind of a bucket well that's a lie Savannah three right at three I'm willing to draw a tree still if there's more than three I'm not drawing a tree if it's two dice what will you do what will your strategy be I heard it back there take chart right if it's too dice you draw a chart certainly if there's eight or nine or 10 or 12 events it's either a bucket or it's a binom PDF and you have to identify by asking yourself do the odds change every time then it's a bucket like cards or you know what if the odd never changes from attempt to attempt then it's a binomial probability distribution and you need to know how to use the binom PDF as well as the longer version of it okay gonna tell you on your multiple choice a couple of questions because I'm trying to also think about if any of this showed up on the non calculator section of the provincial what would they ask I've given you a couple of questions where I'm not actually asking for the number I'm giving you the mathematical expression to pick from on the multiple choice so I'll say which of the following I'm making this up which of the following could be used to calculate the probability of getting two hearts in a row and rather than actually do the number I've done the the fractions or the chooses or whatever okay so make sure you can handle that make sure you can move from calculator approach to oh here's just the simplified factorial approach which one do I want to go with to recognize both all right so first off I'll begin by saying from the probability review are there any you want me to go over there are some nasties on here I did steal some of these from the Alberta Provincial exam so this first group I stole from August 2003 but you will notice a little further on basically in the final third these are from the Alberta exam where it stops having little headings I think that's the Alberta Provincial I think number 19 is the last one that's actually from a BC Provincial the rest are from the Alberta exam and I've already said for Commodore Torch probably they go a little further than we do I'm good with that on the review because the whole goal is you should find the test much easier than the review assignment right so questions you would like me to go over also please remember that I did put my solution key online so if you're stuck I did try and really show my steps on these which ones would you like me to do yeah 1515 okay good question I like this one not because I like this one I like this one I like just because this really lets me cover a big chunk of what we spent the first four lessons of probability on okay how many cards okay tree this one's a bit tricky though because what's the first event the probably the first card is a what and the second card is a that second probability depends because in this case some face cards are also queens okay so here's what I think I'm gonna do with my tree my notation is going to be I'll use the letter F for face card I'll use the letter Q for Queen Kayla here's how I break this up queen on the first draw even though they didn't mention it face card but not a queen on the face first draw neither face card nor queen on the first draw the problem with this one is I have to take into account that a queen is also a face card but if I got a queen on the first draw that does satisfy the first event but that totally changes the odds of the second event because I'm holding a queen already so I think I'm gonna break it up like that by the way what are the odds of getting a queen on your first draw out of four out of 52 so this I expect all you be able to handle how many face cards are there in the deck there's 12 how many of them are queens for so how many non queen face cards are there out of yep no no 8 out of 52 still see the 12 face cards here okay how many others you know what I'm not even gonna bother filling this in because it tells me that it wants the first card to be a face card I'm gonna leave this branch blank it's gonna be a waste of my time now yeah on a written I would never do that on a written I would fill in the entire tree multiple choices I don't get any marks for the tree if you're not using one of the branches and you're pretty confident leave that branch empty now let's keep going queen on the second not queen on the second queen on the second not queen on the second down this branch here we picked a queen by the way I guess hopefully by now you've clued in remember at the beginning I said trees were very very useful this is a fairly nasty question but I'm gonna get it to fall apart with a tree I'm pretty sure how many queens are left in the deck three out of 51 I know this one here 47 I don't care or 48 out of 51 I still don't care here we didn't get a queen we got a face card though like a jack let's say how many queens are left in the deck out of now here's my argument both of these branches satisfy the condition both of those branches have a face card as the first draw queen or other it's still face card and the queen on the second it's one or the other what does or mean and multiply down at a cross this answer is going to be you might have got a queen first queen second or a non queen face card first queen second I have no idea what the answer is but that's that's what it'll be I would consider that a reasonably to me that's a B plus level question although I think once I started going I saw most you guys oh I see just separate because there's some overlap separate the two cases is that right I hope I don't know what the answer is but oh what is the answer hey okay nice little question and I like that just that really combined lesson one two three and I think four okay nasty your question would be given that you have a queen what's the probability that the first card was not a queen but a face card you could do be both over the given one so I that's what why for the conditional probability questions I really just in my mind always say to myself if they use the word given or suppose or if and they're talking they're telling me which branch I am down here and want me to work my backwards it's always both over the given one that mathematically works for me way better than that creepy formula that I always have to run better for anyways next 22 zero okay this is from the Alberta exam and I don't like this question but I still talked about it parts of this I like but as an entire question okay so let me copy it I've debated actually taking it off this review except I did this review on a Mac computer so I only have a PDF file of this on my tablet so I can't edit it and it would mean retyping the whole thing and as much as I like you guys you aren't worth that so that'd be about 40 hours of work no thank you ready says two students performed a simulation that recorded flipping three coins and they did 10 trials so this is the actual trial first of all what's the probability of getting three heads on a single trial so let's see I was sorry part a there is no a that appeared there a what's the experimental probability of getting three heads on a single trial did I get three heads there no no one to the experimental probability is apparently two out of ten I don't think that's the correct answer now if you did this a hundred times you get a much more accurate experiment of probability although nothing would prevent you from getting three heads in a row 100 times is that likely no is it impossible no but if you did a thousand times you'd be even more accurate with your actual versus the theoretical although again nothing would prevent you from okay as I'm looking at this they're talking about flipping a coin heads or tails do the odds ever change I think this is a binomial fact I think on any one of these trials I think it would be binom PDF and I'll fill in this stuff I'll do the choose one here it would be from three flips because you're flipping it coin three times on each trial choose how many heads do you want three what's the odds of getting heads one half how many heads do you want three what's the odds of getting tails one half how many tails do you want zero in fact you know what I don't need to go all fancy because what's three choose three one what's a half to the zero I think I could use binom PDF but I'm pretty sure I can get to just by going point five to the third power point five times point five times point five someone do that point one two five now if I did use binom PDF I would go three flips the odds of success is one half or point five how many successes how many heads three and I'm pretty sure that would also give you point one two five by the way Savannah what's two tenths as a decimal two tenths as a decimal point two so they got a weight they got way too high a percentage the actual theoretical percentages point one two five okay C now C says by the way here was the other reason that I kind of included this is a binomial probability distribution because what does it say in part B or part C use the what okay binom PDF okay now the question is changing just a tiny bit this is the odds of getting three heads on one trial okay how many trials do they want me to do here so it's going to be 10 comma now the odds of success on an entire trial is not one half that was the odds of success flipping one coin what are the odds of getting three heads on one trial what's the odds of success that's what's going to go here and they want exactly two three heads the other reason I don't like this question is it's very easy to get mixed up with numbers because you have the odds of success of a single heads and a single trial I to be honest I might have called this trial ABCD instead of calling it trial one through 10 I don't know anyways that should be the answer I don't know what the answer is but that should be it or 10 choose to point one two five to the two one minus point one two five point eight seven five to the eight and choose to point one two five two point eight seven five to the eight okay those are both get you there although this is a written question this won't be a written question you'll see on your test and remind you before I let you guys go I'll give you a hint as to what kind of questions are great questions any others pretty sure yep yep 19 be I probably have to do a in order to do be just be guessing okay let me copy it and let me also say I love this question I love this question I love this question and what I mean by that I'm gonna tell you right now on your written there's gonna be a question that involves two jars of marbles or something I may also instead of right now picking each jar oh no they did roll a die as well I kind of like that or they can have you pick each jar 5050 but here they rolled a die I have to set up a tree and walk through part a before I can give you a good answer for part B and then I'll answer your question for part B because you're wondering about how you know which is the given right given what so it's going to be given white no Eric Bing didn't find that mistake are you serious I made a mistake I'm mortified if I did I got a and white I got given that it's white given that it's white is that what it says online I think it should be I think I'm right okay let's walk through the whole thing okay before I get to their tree so we have two events pick a jar pick a marble okay the other way that I can do this is instead of having you pick a jar pick two marbles from one jar jar one jar two red white red white to pick a jar it's not 5050 instead it looks like it's going to be two out of six and four out of six because we're rolling it die yeah okay with where I got that Sam how many red balls are there in jar a how many red marbles out of and seven out of 12 in jar B 8 out of and so part a find the probability that a white is selected part a is going to be that branch or that branch it's going to be 2 6 times 7 12 2 over 6 times 7 over 12 plus 4 over 6 times 4 over 12 6 times 12 is 72 I think it's going to be 14 plus 16 is it 30 over 72 I think that's what you get is that right and then divide by 6 5 out of 12 is that what I said the answer was in my answer key yes I did now let's go through yours got it okay let's continue B so Kayla whenever I see the term given or suppose or if I always ask myself if what suppose what given what given that it's white find the probability that it came from jar a and what I've told you is that's going to be both all right a and w just like the restaurant all divided by the given one W okay now the given one W we've already done right here because didn't we figure out the probability that it's white that won't always be the case in fact I think on your test for one of the questions I didn't walk you through part a I just went straight to part B as your question there was no part a part B I simply said blah blah blah blah given that and I launched right into conditional and I'm assuming that you're going to figure out oh I better it's both over the given one calculator mistake Kayla okay a and w a what did I say jar 1 and jar 2 I should have said jar a and jar B that's silly a and w that's going to be 2 out of 6 times 7 out of 12 and I get 14 out of 72 divided by 5 out of 12 how do I divide by fractions with multiply or you can go straight to your calculator you want to be careful if you're going to your calculator you can't go 14 divided by 72 divided by 5 divided by 12 it doesn't know that that's one fraction you've got to use brackets you're not going to get the right answer you need to go 14 over 72 in brackets divided by bracket 5 over 12 that's how it knows you're going one fraction divided by another fraction and then if you hit math enter enter you find the answer is 7 over 15 you're totally going to see something like that on your chest something along those lines next 22 who has 22 so right sir the you're looking my answer key at all or no I'll walk you through it on there so here's what I said this is by the way from the alberto one this is probably a little trickier than we feel comfortable asking you here's what I said here's the total number of ways to mix up the letters in the word Canada six letters divided by 3a 6 factorial over 3 factorial I said the total number of permutations is 120 and that's permutations with no repetitions because I divided by 3 factorial how many of those will spell Canada one it's one out of 120 I didn't go too fancy there and I kind of think outside of the box my usual methods didn't really work but I said I can if I can count it I can figure it out let's fall back on day one when we define probability the total number of successes divided by the total number of outcomes that okay you make it there next 30 the mice I'm not going to copy the picture because that's not going to fit on my screen so we're looking at number 30 who asked there 30 Kayla you did I'm looking at the answers that they gave me the zero the one in the two fractions or decimals looking at the answers that they gave me the zero the one in the two these ones here fractions or decimals I'm already kind of wondering if this is some kind of weird by no PDF type thing because it's the four decimal places it's kind of looking like some of the answers that I wrote let's find out okay so we have yellow mice are genetic mutants and they're breeding produces offspring that may not survive of the offspring that do survive one-third are great so zero out of four are great if this was a binomial probability distribution it would go like this binom PDF from four mouse what's the probability with a gray mouse comma how many mice do we want to be gray in this first one here see if that works out to point one nine seven five let's find out four comma one-third comma zero ah it does you know what this is a binomial probability distribution function now how did I figure that out how many mouse mice grandpa four not a tree okay so I eliminated that then I said so this is either a bucket or a binomial do the odds change I don't think so I don't think whether or not the previous mouse was gray as any effect over whether or not the next one breeds gray or not so I said you know I think the odds don't change and I said if nothing else I'll at least try it because it takes five seconds to type into my calculus now my guess is confirmed and I suspect this question this was on the Alberta exam was considered a little too tough and so to make it easier they said hey why don't we give them a couple of the answers and that way they can kind of check to see if they've guessed right okay now let's keep going three out of four this would be binom pdf of four comma one-third comma three point zero nine eight eight and four out of four is going to be binom pdf four comma one-third comma four could have just gone second function enter mr. Duke the point zero one two three point zero one two three four five six seven eight I'm guessing I'm assuming there's a nine over here in the calculator around in eight up to a nine kind of an odd probability but I think that's the answer to hope okay you see I put all that together I kind of tied together a lot of little hints in the question and you know what else I didn't do I didn't let the wordiness of this question overwhelm me I'm gonna be able to do this oh they gave me some answers let's see if I can get the same numbers as them somehow using the skills that I have next 34 okay 34 I do like I think this is fair game this would be an Alberta question that I'm totally good with how many power plants grant total 11 tree no no so this is either bucket or binomial let's see says the probability that any one will not be functioning is point one and exactly three this is the wording of a binomial question I'm pretty sure and I think the probability of success is point one probability of failure is point one let me copy this puppy how many power plants that's one right it's not a tree process of elimination so if it's not a tree it's either bucket like using combinatorics or binomes so the real trigger then is you ask do the odds change here or not if the odds never change from step to step it's binome PDF if the odds change like in a card question oh I picked a queen and now there's only three left in the deck I picked another can only two left in the deck that's a bucket choose this is gonna be binome PDF 11 comma point one comma three or eleven choose three point one to the third point nine to the eight eleven comma point one comma three D is that a hand up Caitlin are you hitting Regan go ahead this one was tough 33 was yucky 33 is yucky enough Priya I'm just gonna go to my answer key so here's what I said child has two quarters two dimes and three nickels he's picking two coins I probably could have done this with a tree but I had a tough time wrapping my brain around it I said well look if I have two dimes two quarters and three nickels and the question wants me is asking what's the probability of the two coins that I select well the total value at least above 35 cents I thought about it I looked at all the coins that I had and I said you know what there's only two ways I can break 35 the two ways that I can break 35 are two quarters or I can tie it quarter and a dime any other combination of coins is less than 35 cents think about it for a while but try it you'll just find nothing else works so I said you know what I think this question really is wanting me to find the probability of two quarters or what is or me at quarter and a dime so then I said I can do this as a bucket from two quarters to choose two from two dimes choose none from three nickels choose none that's that one or from two quarters choose one from two dimes choose one from two nickels choose none all of these are over seven choose to double check plus plus seven plus plus two plus plus plus seven plus plus two having said that I think you could have done it as a now as a tree quarter on the first not quarter on the first sorry quarter on the first dime on the first nickel on the first and then quarter down nickel quarter down nickel you'd have three times three to nine branches at the bottom it's doable and then simply put a check mark under whichever ones are above 35 cents that would also get you there so Steph is asking will there be a question I guarantee there'll be an at least or an at most question okay so instead of this which is a bit confusingly worded I would have no problem for example saying if you're picking two picking four cards what's the probability you get at least three jacks which would mean three or four I will in just a second okay so yes for absolutely at least or at most or more than or less than kind of questions fewer than 35 yeah 35 I like I think so so Pat here's the answer to your question you know okay read the question to yourself I'm pretty sure I said to yourself how many boxes are we looking at one how many candies in the box how many tree okay so this is either binom or choose says the probability of the black candy is produced is point one two does this seem to suggest that the odds change at all I think this is a binomial probability distribution function because I can't think of a way where it'd be like like I think it's just whether the machine puts that candy in there or not okay Laura what's the case that we have here what do they want us to find the probability that it contains what no no no no no no no no no no no did I go on a ranch earlier about being careful to read the questions very very carefully at least five that's a hugely important what does at least five mean what are the cases give you a hint five at least okay you ready if we can't do the vocabulary or not give you all do the math five or or or or or although it to 60 clearly they don't want me to do that I think they want me to use the complement and the CDF function here's what I would do probability of five or more that's one minus the probability of four or less it's going to be one minus the binome C because we're doing the cumulative we want an or less cumulative distribution function of sixty candies point one two chance of getting a black candy for or less because we're using cumulative one minus when I'm CDF of sixty comma point one two comma the odds of getting more than five pretty good 86 percent the nearest hundred sorry point eight six one eighty six point one percent let's see bright well point one two if the odds of five candies making sixty boxes and the odds are about ten percent each time so on average I expect out of sixty boxes there to be around six here we got five yeah you know what I'm okay with that answer looks about right to me give or take next come on Mr. Duke wake up number thirty thirty three twenty three two three okay hockey arena this one okay so hockey arena is has seating that's divided to sections led it from a to z inclusive and a a to xx inclusive so each section consists of 20 rows with 16 seats in each row at a sold-out hockey game it's announced that a prize will be given to person setting in section j day what's the odds that you win a prize here's what I said there are 26 rows times 16 seats there are a total of 320 seats in section double J the odds of you winning is one in 320 if they're giving one prize away and I'm in that section I would look around who all is around me and I got one chance out of that many again that's a bit of a strange new word in one next okay then a few hints here's you're gonna see on your written section in no particular order a Venn diagram question how do you recognize the Venn diagram question often percentages only two outcomes categories fill in the middle or fill in the middle which is both and the overlap or put an x there and work your way out to solve for x guarantee one of those guarantee a bucket card question so instead of just two cards which you can tree your way to five or seven or something like that please read careful it's gonna be at least one at most or at least kind of question list the cases because only a couple of them and do many of the atom up if it's a bunch like 10 you can probably complement your way by going one minus the other num the other option the other outcome conditional probability it's either gonna be bag of marvels factory defective question factory a and factory b 30 percent are made of factory a 70 percent of made of factory b 60 percent of factory bs are defective 40 percent of factory a's what's the probability given that it's defective that it came from factory a or factory b disease question the life saver one the test was 98 percent accurate but as it turned out the person only had a 65 percent chance of having the disease at a better than one three chance of not having it we're way better off than 1% or the other one I've seen has been a conditional condition conditional binom pdm Caitlyn the probability that Caitlyn plays with her hair in any one minute is 80% given that she's played with her hair six times in the last 10 minutes what's the probability that she's played with her hair eight times in the last 10 minutes given that she played with her hair it's at least six times in the last 10 minutes what's probably she played with her hair eight times you didn't like that one for me I did make that up 100% okay binom pdf and binom cdf also make sure you know the choose notation as well what's the choose notation and choose x p to the x q to the one minus x but with numbers there make sure you know on your calculator it's binom pdf of n comma p comma x at the syntax you know how to use that stuff the written is pretty short the written only has five questions most of this test is multiple choice I don't really multiple choice questions mr. 14 so 14 multiple choice other things you need to know terminology there are two key terms that we've used mutually exclusive and independent what does mutually exclusive mean ah that's it that's the best non-math definition no overlap Pat what it also means is this the probability of a and b is what you know two items are mutually exclusive what's probability of a and b occurring at the same time over complicating it if there's no overlap what's the probability of a and b occurring at the same time nothing can't happen because no overlap it's saying in your Venn diagram the very very middle part has nothing in it what about independent well that meant the odds don't change what I really said is a built-in handy-dandy check is if you're doing a tree a not a be not be be not be if they are independent this number and this number will match because what it's saying is hey the odds of whether a occurred didn't change the odds of what it be occurred they're independent of each other third term that we used a complement what's the complement I mean says that's when I say nice thing no Lorentz for talking with the mathematical term what's the complement if the probability of a occurring equals lowercase letter p the complement is the symbol is probability of not a and it's one minus the probability of a occurring Stephanie if the odds of you failing math 12 was point six what would be odds of passing math 12 point four complement and remember sometimes it's easier to solve for the complement and go one minus get the actual answer that you are looking for at least one question on your test where complement will work way better you can brute force your way to that least direct most question you can brute force your way to it and add them all up step by step by step looking at all the cases or you can just clue and you know what I'll do the opposite to track from one where is left must be what I'm looking for hopefully remember the whole concept of the tree or means add and means multiplying otherwise I think it's a pretty straightforward test no big surprises anything else that I've forgotten that someone was wondering about I don't know yet what your final schedule is going to be I'm still battling as soon as I know I'll email you guys a schedule I hope to have it for you for Thursday I hope