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Outcomes, The Counting Principle, and Theoretical Probability

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we've been talking in chapter 12 about statistics and probability and today we're going to talk about a couple of topics then I'm going to call outcomes and Theory probability we're going to deal here with scenarios where there multiple possible outcomes and we're going to talk about what possibilities there are outcomes by the way just what's the number of possible ways that a scenario could or can turn out so if you're rolling a die how many outcomes are there well there's six right you could roll the one you could roll it pets Etc if you're flipping a coin you've got two different outcomes heads or tails and if you're pulling one random card from a deck of cards you got 52 different outcome this is not difficult what you also need to know is the phrase sample space sample space is the list of possible outcomes that might happen it's making a list of those number of outcomes so we would make a list of ace of clubs 2 of clubs three of clubs Ace of Diamonds 2 of add a bubble that this list would be really long and you can see a picture of it right here now the sample space for flipping coins would be pretty crazy heads Tails your list only has two different outcomes on it and if you're rolling a die you've got a sample space of A1 or A2 or 3 or 4 or 5 or 6 not too difficult to understand the idea of sample space it's just a list of what could happen now speaking of what could happen this morning as I was getting dressed lots of things could happen I had all these different sweater vests to choose from and I had four clean shirts to choose from how many different outfits could I make here if I've got four shirts and six sweater Fest how large would my sample space be of possible sweater vest shirt combos in other words if I made a list of black sweater vest blue shirt black sweater vest white shirt black sweater West grey shirt black sweater vest other form of grey shirt yellow sweater vest white shirt Etc where at cetera would be pretty boring to make that list but if all I wanted to know was how large the sample space would be just a number of possible outfits I need to actually write out the sample space I could figure out the number the size by just doing this take your 6 sweater vests take your for sure multiply those two numbers together and that will give you 20 for possible outfits and I know that they're 24 without having to list them all stop okay that's pretty convenient  now it's probably important for me to wear some pants today too so how many different outfits can I make when I put pants into the equation well it's still sick sweater vests and four shirts and I'm still going to multiply those together but now I'm in a x 2 for the two pairs chains they're actually 48 different outfits that I could make using these items of clothing this is something called the counting principle fundamental counting principle or sometimes called the basic counting principle and what it says if you want to know the number of outcomes just multiply all the numbers together you might have I know that but if you didn't now you do know it and this is actually really powerful tool in math you can find out the number of outcomes just using multi what about shoes what if I have my black chucks or migrate checks or my kind of slightly greenish checks now I'm going to have 144 possible outfits because it's 6 times 4 times 2 times 3 and you can check them after yourself on that if you would like to what if I wanted to know how many different possible phone numbers there are  in the United States of America where we generally I have a 3 digit area code followed by three more digits and then a dash and then four digits after that well let's go digit by digit the first number of your area code could be any of 10 different digits because it could be one two three four five six seven eight or nine or it could be a zero I don't know if any area codes actually what was 0 but it could be how many different numbers could II digit be there could be 10 different digits that can go there too and when did 10 different digits I could go there and 10 different digits that could go there and 10 + 10 + 10 more + 10 10 more and then oh my gosh how many front phone numbers would this be well if you multiply that out it's going to be 10 to the 10th power so how many different possible phone numbers are there in this Addax scenario there are about ten billion know exactly 10 billion possible phone numbers in the United States of America  okay how you get to try this I'll make it slightly easier for you how many different 5-digit zip codes are there possible bet you can figure that out right alright now that you figured that out let's talk about Monopoly you've all play Monopoly right let's see your who you're playing Monopoly and you're on I think it's New York Avenue and no let's say it's the one right before that and you really want to get to the free parking so you get some cash but y two spots away you've got a roll of Snake Eyes How likely is it for you to roll snake eyes probability of you getting one one on your two dice well here's the sample space when you roll two dice you can get 11121 314 what do you get three three you can get for four you can get for six you can get for one you could get six three there's a whole bunch of different things actually there's 36 different out consider possible when you roll two dice number cubes  what are the chances of those two numbers both being a one what who won out of those 36 items in the sample space are snake eyes so you have a 1 and 36 chance of getting for once  now if you don't want to bust out a sample space diagram every time you play Monopoly you can actually figure out that you have 1 in 36 chance using the counting principle let's take the first I don't you have a one in six chance of getting a one  and don't you have a 1 next chance of getting a 1 on the second day  well if you multiply those together you got one x one on the top and you get 6 type 6 on the bottom so that who's you that you have a 1 and 36 chance  what is the counting principle works for probability fractions just like it works for finding the number of outcomes alright so what's the probability of flipping heads 3 times in a row well on your first coin you have a one in two chance on your when you have a one in two chance on your third coin you have a one in two chance so on top you have 1 * 1 * 1 * 2 * 2 * 2 so you haven't any chance who's that particular occurrence taking place all this is is multiplication it's really easy alright so here's the last challenge if I were to pick out an outfit completely at random I turn the lights off in my closet and is reached randomly at things what are the chances that my sweat nice shirt would be great what are the chances like give me a fraction for probability or give it in a percent or decimal to if you wanted to but what would my probability be  alright once you figure that stuff out you got the basic idea hope you enjoy this video and I'll talk to you later

Uploaded by Jeff Marbut.

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Outcomes, The Counting Principle, and Theoretical Probability

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