 here we go a bag contains 10 red six green and five white marbles determine the probabilities of the following okay the first one drawn is white I think that one I don't need to do a tree for the first one is white five white out of how many marbles grand total what's the probability of that five out of sorry 21 okay be the second one drawn is white given that the first one drawn was white and there is no replacement and here's what they're saying find the probability of the second one given that the first one drawn was white okay suppose the first one drawn was white now we're on the second pick how many white marbles are left in the bag four out of and you know what they're talking about I think in my tree where I have white green red white green red white green they're talking about that number right there okay and yeah four out of 20 lowest terms one of thought yeah point to sure event a is defined as the chance that it will be sunny tomorrow zero you say well we're getting there we're getting closer if there is an 18% chance that it'll be sunny tomorrow what's the per probability of not a as a percentage 82% compliment very very useful skill hopefully ready realized how handy that can be question three in question three I see percentages and I see both I'm going to use a Venn diagram if you did this with the formulas great but I'm going to go like this we have hamburgers pizzas both was 40 I guess that means I'm going to put a 20 there there's my 60% liking hamburgers I guess that means I'm going to put a 30 there there's my 70% liking pizza what do all four areas have to add to but the percent it's got to be out of a hundred so I got 60 30 90 you know what gotta be 10% there and neither is 10% I would get there with a Venn diagram by the way neither is not or so if you did this with the formulas you would do or which is one plus the other minus the overlap and then compliment number four this is a reasonably tricky question you know what I'm going to fall back on a sample space if I could count it I can solve it so here's what it says a game begins with two cards being dealt from a standard deck of 52 cards there's my two cards to win this game the next card dealt must be the same as either of these first two cards or fall between them if the first two cards are a three and a 10 what's probability winning the game alright if I dealt two cards and I'm picking a third card how many cards are left in the deck what's this going to be out of at least I've picked to 50 cards left in the deck right here they are what's left how can I win if I get another three how many more threes are left in the deck or what does or mean if I get another 10 how many tens are left in the deck or if I get a four five six seven eight or nine how many cards is that four five six seven eight or nine well right now how many is this six and how many different suits are there I think it's six times four I think there's 24 different four five six seven eight or nines I'm gonna just count and I'm gonna say you know how many different ways I can win out of 50 that many ways there may be a way to get there with a tree okay I for one card I can count three out of five apparently 36 really really each of the 11 letters of the word mathematics is placed on a separate card a card is drawn and not replaced and then a second card is drawn what's the probability that they're both vowels how many cards are we picking here to okay probably now I'll go to a tree for one card like the previous quite I'll count two cards tree and I think it's gonna be vowel not vowel vowel not vowel but I'll go vowel one not vowel one vowel two not vowel two here's my tree vowel one not vowel one folks little chatter back there thank you vowel two not vowel two vowel two not vowel two what are the vowels a e I oh and you how many vowels are in the word mathematics one two three four four out of 11 anyone besides David 36 is 11 okay how many non vowels David 7 out of 11 okay down this branch we picked a vowel how many vowels are left and you know what since all they wanted was vowel one vowel two do I really need to fill in the rest of the tree I might on a test just to do my checking error add to one add to one but you know what this is a simple enough one I'm pretty confident I think it's gonna be four oh let's write the statement just in case they show that probability of vowel one and vowel two is four out of 11 times three out of 10 12 out of 110 whatever the heck that is the lowest terms I don't care could you have done that without a tree you know what now that I think about it because it's the same event twice in a row I probably could have visualized that particular branch okay number six how many cards number six how many cards one so I'm going to fall back on frequently just counting because I know what a deck of cards looks like I'm not going to be doing a tree here because tree is for two separate events uh getting a heart 13 out of 52 one quarter b getting a face card 12 out of 52 c getting a 10 4 out of 52 I'm just counting oh not b I'm not going to count I'm going to use the compliment 40 out of 52 yes okay a or b so here is one of the only times I'll use the formula because I don't have a picture of a deck of cards in front of me this is going to be a plus b minus a and the or means add minus the overlap it's going to be 13 out of 52 plus 12 out of 52 minus and I'm just going to count I know and means multiply and means multiply when it's separate events not when it's one card so now we're fine tuning our definitions how many cards our face cards and hearts at the same time yeah three out of 52 hope you said three sure you did uh it's 13 plus 12 25 take away be 22 is that right out of 52 so for a single card draw as I fall back on if you can count it you can solve it yeah use the formula occasionally uh a and c okay not and means multiply here we're not doing a tree instead how many cards are hearts and tens at the same time I think isn't that the 10 of hearts right how many 10 of hearts are there in the deck one out of 52 g a or not b okay this is going to be a plus not b minus the overlap it's going to be a 13 out of 52 plus not b oh 40 out of 52 minus okay ready how many cards are hearts and at the same time what does not be mean how many hearts are not face cards that's right that's what you know what I'm going to cheat I'm not going to count them I'm going to say there's 13 hearts altogether how many hearts are face cards so how many are not ah 13 plus 40 is 53 by the way I would know 53 out of 52 was the wrong answer because can I ever have an answer bigger than 100 percent don't think so oh it's guaranteed to happen and then some but my coach says I'm supposed to give 110 percent that's bad math anyways 53 take away 10 43 and the last one not a and not b okay how many cards are not hearts and not face cards well first of all how many non-face cards are there in the deck 40 how many of those are hearts I think 10 because there's four suits so how many are not hearts I think 30 by the way do you see I complimented twice to get that I could have gone forwards I said you know what this is going to be easier I know there's 40 face cards and it's 10 10 10 and 10 sorry 40 non-face cards there's 10 10 10 and 10 so 30 of them are not hearts okay didn't didn't go fancy there Brett just count it that's a tough one though gotta be honest I really have to think about that one mark for each of those turn the page okay question six how many dice in this question two chart for dice remember we did the six by six dice chart I'm gonna do this is a often what they'll do because six by six is a lot of handwriting they'll give you what they call a tetrahedral dice four by four so I'm gonna have this the first dice you get a one two three or four and you have the second dice you can get a one two three or four so here is my chart I could get a one one one two one three one four two one two two two three two four three one three two three three three four four one four two four three three or four chart Nick takes even for a six by six set of dice really 30 seconds probably well worth the investment especially because I notice there's an abcd you know what then it's really worth listing them all because then we can fall back on our counting by the way what's each of these probabilities going to be out of how many outcomes are there 16 right boy that table's having some bad bad karma there okay what's the probability that the sum of the two dice is equal to six I think that's this one or this one or how many now I'm going to erase those so I don't muck up my diagram but yeah I'm pretty sure it's three out of 16 b the product is a multiple of three what does the word product mean okay when you multiply these together three goes into it what's the only way that three will go into it I think if one of the original factors is three I think really what they're talking about is all these ones and all those ones I don't think any of the other ones work how many seven out of 16 right if you can count it you can solve it the number on the first die that's the here is bigger than the number on the second die so the way I've drawn this it looks like the second number is the first die kind of a dumb way for me to write it but that's okay what this is asking me in my chart is in which of these is the second number bigger than the first number uh here here and here how many so if you did your first die here and your second die there you probably got the bottom corner circles are colored in uh one two three four five six and again we're not using a formula we're just counting six out of 16 the sum of the two dice is equal to six or the product of the two dice is a multiple of three here was my sum equal to six here was my multiple of three right there how many one two three four five six seven eight is it nine yeah or I could have gone uh one plus the other minus the overlap I could have used the formula too but I can count nine out of 16 E what's the word after four conditional last day's lesson I gave you what I thought was a handy dandy easy way to remember this first of all this is the probability I'm gonna now this is the only time I go to formula what's the given what's the given not four what did they give me and you got to translate the English grammar here okay sum is six what do they want me to find first begins with a four and that's going to be both over the given one now the given one is the sum is six I think I calculated that already did I not look at your answers what was the probability that the sum was equal to six I've scrolled down but was it three out of sixty yeah okay what's the probability that it adds to six and the first dice is a four so here was the ones that added to six how many of those also added to four sorry how many of those also started with a four now I'm going to circle this one because I put the first dice at the end like a complete idiot but you know what how many have a yellow streak and a red circle on them one out of 16 there's the probability that you started with the four and added to six divided by the probability that you added to six both over the given one how do you divide you know what I think when you go how do you divide by a fraction flip it and multiply you get that now here's the short way we could have done this one Jen how many have a yellow streak through them how many are circled out of see it you could if you already know you're on this yellow streak what's the probability that it started with the four that's really what that last question was saying the one out of three actually jumped out at me in the diagram I probably could have solved that without the formula intuitively but usually for conditional I don't have a formula so what's this quiz out of I think I went one mark per let me one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen one mark per by the way he was sneaky I normally don't give you a quiz on the topic that I just taught but it was such a nice way to reinforce the topic I left it on there in previous years I've made a little one mark bonus no I'm gonna say was fair game for one mark on a take home quiz give us a score out of nineteen please and when you're done pass them in so before we move on before I turn you loose the OJ Simpson trial one of the most famous ones actually last century so OJ was charged with killing his wife and although there were various defense tactics the prosecution had a major strategy their main strategy was OJ was a spousal abuser which was documented they had 911 calls and defense didn't try to deny that so OJ beat Nicole therefore he was much more likely to kill Nicole and they were pounding that he hit his wife he killed his wife he hit his wife he killed his wife the OJ trial was not going good at the time he had Alan Dershowitz and Robert Shapiro as his attorneys two of the most high priced attorneys in the U.S. and then he brought in a name you may have heard Johnny Cochran and Johnny Cochran right away he wanted to remove this oh OJ beat his wife therefore he killed his wife strategy so here's what he said right now we have the prosecution and the prosecution is saying given that OJ beat his wife the probability that he killed her is high the defense Johnny Cochran came along and he said wait wait wait wait wait I have reams of statistics and in only one percent of spousal abuse cases does it end in murder so he said this the probability that given that there is abuse the probability that murder occurs well he says if only one percent of the cases end in murder the probability that OJ is not the murderer 99 chance OJ is innocent the numbers aren't quite this high I'll show you the article but this was his point with the jury spousal abusers don't kill their husbands spousal abusers so don't don't don't don't kill their wives spousal abusers don't kill their wives it's true very very very few domestic abuse situations end in murder but the prosecution missed out because the correct conditional probability statement should have been this given that you have a husband beating the wife and given that a death has occurred what's the probability that the husband is the murderer you see the extra step there any five percent of the time the husband did it it's by the police always look at the husband right away sadly had a fairly famous trial quite recently in Surrey where someone claimed that his wife had been killed and suddenly reported her missing and suddenly it turned out to be the guy that reported her missing was down guilty just a few months ago right so had they had a mathematician on their staff the odds are pretty good OJ might have been found guilty I actually even found the article I was where is it base formula and OJ Simpson I'll show you the actual percentages they aren't quite as high as I said and already you can understand most of this you're going to see hey that's conditional probability by the way what's the symbol for and I told you I use a comma what's the actual symbol for and an upside down you it stands for intersection overlap it's the bend diver okay fine so they're using different symbols but can you see it's and and both of the given one same equation we've been doing let's look at OJ Simpson so if we really quickly Alan Dershowitz if you read this right here it says he stated that only oh it was even smaller 0.1 percent of men who physically abuse their wives end up killing them so that means it's a 99.9 percent here the compliment chance that OJ was innocent as it turns out if you do the conditional formula given that a death has occurred you see that number there 81 percent of the time the husband did it not 90 percent chance 99 percent chance of innocence 81 percent chance of guilt I love conditional probability very counterintuitive you have the remainder of class to work on the homework from last day I'm done