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Algebra Lesson 0-11 Simple Probability & Odds

Added Sep 05, 2017 •

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lesson 11 on simple probability and odds we have a few definitions first of all to find the ability of an event you put the favorable outcomes over the turtle the probability of Anna what is the ratio of the number of favorable outcomes to the total number of possible outcomes for example when you go to die there are six  possible outcomes 1 2 3 for five or six these are called your sample space  so if you're asking when your sample space will be heads and tails  if you have a bag of 10 marbles to Blue 3 4 green and 1 purple that will be your sample space so the sample space is all the possible outcomes and then probability will always be some answer between and one  if the probability of something is zero that means it's impossible to happen and if the probability is one that means it is certain to happen so the probability of rolling a 7 on a number cube is 0 the probability of getting heads or tails on a coin  first one to get one of the what is certain to happen there's nothing else possible  so probability is going to be anywhere from 0 to 1 include 0 and 1 that's what inclusive means including so what I do it needs ample  feeling with probability I bet you guys can already do these on your own Dyersburg find the probability of getting a 1 or 5 how many ones or fives on a number cube out of six and we want to reduce that remember to do these with me and probability of rolling an even the other three out of six three numbers or even out of six and that reduces to one pamer going to skip over the you tries what is a compliment they give an exam full of what a complement is that's not the kind of compliment I cannot for thank you very much the events for failing a 1 and 4 knots rolling a 1 are called compliments the probability of rolling one is 1 out of 6 the probability of not rolling one is the other five out of six so those are called compliments  the sum of complementary events will always be one one + 5/6 is 66 or 1 so the compliment is just the the other or what's left an example to for example to a barrel contains 5 red chips 7 Blue Chips sits lower chips and 10 Green Ships one trip is randomly drawn find each probability so the probability of drawing a blue chip how many blue chips are there 7 out of  the total 12 + 16 is 28 28 South 716  yes and then we can reduce that 214 probability of pulling a blue chip out is 1 out of 4  now that's a beer radically correct field local probability experimental would be if we actually did it we actually have this bag of chips so in theory every four chance we pulled out will be blue okay if we actually did it with that happen maybe maybe not the more you do the experiments the closer it gets to what would happen in theory I was looking to see they talk about that here they don't call the law of large numbers that the more you do the experiment the closer your outcome with Tom's you what should happen in theory or yellow how many Reds and yellows that's 11 out of 28 and that does not reduce so we would leave it  animals are the probability of knots green so if 10 are green how many are Knott's green the other 18 what is a question dealing with complementary events and we can reduce that by 2  14 Gap M14 question so far we're going to skip over the you tried  and talk about what a tree diagram is it is a open for counting the number of possible outcomes so they have us do all this what can make a tree diagram and then they teach us the fundamental counting principle which eliminates our tree diagram but they want us and where the fundamental counting principle is coming from so we're going to practice a tree diagram first  MMO they more efficient method of doing a problem  without the tree diagram pets example 3 let me refill baseball caps come in blue yellow or white  the cats have either the school mascot or the school's initials use a tree diagram to the the number of different cats possible so you can get the cap in blue yellow or white  and then you can get either the mass or the school initials so this is what a tree diagram of a flight for that situation we have blue yellow or white and I mascot initials mascot initials mascot initials so you can get a blue cap with mascot beer cap with initials Yellow Cap with mascot Yellow Cap with initials White Cap with mascot for white cap with initials cigar 6 different possible caps using a tree diagram BC another way to get six without having to draw a tree diagram  yes and this is called me from Dental counting principle we have three different colors and then two options for the cat so if you multiply those abilities  you get your result  but I have to go to the next page of the rated the third tree diagrams  so this is called the fundamental in principle it relates the number of outcomes to the number of choices so amway's times in Waze Suburban three colors of hats  and then two different things we can put on hat we take three times too and we get six outcomes this is called the fundamental counting principle  and much more champagne drawing the tree diagram every time suburban and Abby for example for letter A says an ice cream shop offers one two or three scoops of ice cream from among 12 different flavors ice cream can be served in a waffle cone sugar cone or cup is the fundamental counting principle to determine the number of possible choices so we have one two or three scoops there are 12 flavors that I read that part  12 different types of ice cream cast from mm3 difference whatever's to put it in two cones in a cup so we multiply play by 12 by 3 remember you can multiply those in any order so you can do 36 x 3 or you can do 9 * 12 and you get 108 different options and let her be says Julie needs to make a 3 digit password for his log on turn on a website the password can include any digit from 0 through 9 but the digits may not repeat possible 3 digit passwords are there  so digits you can use a digit from 0 to 9 so how many digits is that  10 0 1 2 3 4 so there's actually 10 what is there so he picks his first digit he has 10 optionfair but then you can't repeat so that means he only has 9mm Eights  so 10 * 9 is 90 and 90 * 8 720  720 different options three digit passwords questions on that almost done then the end of the lesson talks about aunts what that's all you try  alright so what are arms the odds of Anna what are the favorable outcomes to the unfavorable so winners over losers at all sometimes Survivor band total rather than favorable over total which is probability odds is favorable unfavorable so the numerator and denominator here should add it to be 1 before you reduce if there's five different outcomes and chewer winners and that means how many are losers 3 so they will find out two or winners three losers what's 2 + 3 add up to be the total to Winners 3 okay well as if we were fighting the probability it would be 2 out of 5 do see the difference alright so example 5 find the odds of rolling a number less than 3 how many numbers on a tire Less Than 3 show so how many are knots Less Than 3 weather for search numbers on a die all less than three they will be winners if we're old one or two we win if we roll for five or six removes so the other that's running or 2 to 4 or 1 to 2 one chance that we win for every two chances that we lose  questions but you guys go ahead and try this one got a little time left  stay rolling a number greater than 2 Plus  don't forget I'll be checking your notes when we take the test on Thursday  so make sure you got all your notes in one notebook title  included definition examples  how many numbers are greater than 2 on a number cube  whole numbers into how many are not greater than yes so our answer would be to one so Peyton reading your questions when they ask for probability it should be able Turtle when we're asking for odds it's winners to losers okay Right Stuff

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Algebra Lesson 0-11 Simple Probability & Odds

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