Hi and Welcome to Probability and Statistics Tutor. I am actually very excited to teach the class because a lot of people over the years have asked me to put this class together and I finally had the time to do it so I am really excited to share it with you today. And what we are going to do is we are going to cover probability first then we are going to move on into statistics and cover by and large most of the topics you will see in your class.
Now a lot of people have problem with probability and statistics usually for a couple of reasons. The first reason is that every single problem, almost every single problem that you are going to see in this class is basically going to be a word problem. And that just turns a lot of people off from the beginning because instead of just being given a problem to solve in a concrete rigid way, you first have to read the thing and you had to figure out what it is asking you, pull out the information, figure out how to attack it and use your logic what you learn in the class hopefully to attack the problem. So what is that really means is every problem is different. It is not like when you were learning your algebra way back along time ago how to solve an equation. That was new and frightening to you a long time ago and you got the hang of it because once you learn the rules, really it is very mechanical after that for algebra and for calculus and even trigonometry and all that stuff.
Once you learn the rules, you just go step by step through them, mechanically turn the crank and get your answers out. But in probability the math is by definition very fuzzy. You usually do not get concrete numbers to everything. You get a probability that something might occur. You are not necessarily going to know if something is going to occur or something is not going to occur but your are going to get some sort of probability or some number that represents how likely something is to happen so it is not really that math the we are used to dealing with growing up that one plus one is two and it is always that way. You shuffled a deck of cards, what is the probability you might pull some cards out of the deck. It is not the kind of math that we usually all deal with growing up on a regular basis so it is new and it is different and to a lot of people, it does not seem very rigid and very mechanical once you learn the rules. We are going to change all that and the way we are going to do it is we are going to start at the beginning, teaching you step by step what every definition means and working a lot of problems so that you can get your brain wrapped around how to attack these things. So we are going to this one step at a time.
In this section, before we actually get to probability, you have to start somewhere. You have to start with the foundation. So this section and actually the next section does not actually have any probability in it. It is laying the foundation for that. Really when you start your class, one of the first things that you learn about are these things called permutations and combinations. They are going to be important when we go on to learn about probability and statistics so we are going to take some time and really understand what they mean. We are going to work a lot of problems.
So what do you think the word permutation means? I think we have all used the word before. I think you a basic idea of what it means. Permutations are kind of like an ordering of something. It is a specific order. You may have a red sock, a green sock and a blue sock and hat might be a permutation and order of those socks laid out on your bed and you might flip it around. You might have a yellow sock, a green sock and a red sock. It is the same socks, they are just in a different order. That is a different permutation. That is what a permutation is. I want you to burn that in your head. I am going to say at about 50 times in this section. A permutation is an ordering of events when the order matters. Why the order matters, it is very, very important because in the next section we are going to talk about something else called the combinations where the order does not matter but just put that on your back burner for now. Right now we are talking about permutations where the order does matter. So it is really easiest to understand really what this means if we take an example. So what are we going to do is we are going to run a marathon.
We have four people in this marathon and they are running a marathon so somebody is going to win the race. He is going to be the first or she going to be first and there is going to be a second place winner and a third place winner and a fourth place winner because in this little example I have given, you only have four people. So we are running a marathon first, second, third and fourth. What we are going to find out and what are we going to ask ourselves is if I am only concerned with first and second place, how many different ways can first and second place occur? That would be basically asking the question how many permutations are there for the first and second place winners when I have four people winning the race. So let us look at it. So what you are going to have, we are running a marathon and you are running this marathon so there is going to be a first place winner and there is going to be a second place winner.
By the way who is running in this race? Okay we have four people and their names are Jason, and Sean and Sally and Martha. So all we are trying to do, we are not even doing any math here, we are just talking about the marathon. So we have four people and these people are all running in a race and on a given day, Jason might win and Sean might be second place and on another given day, Martha might win the first place and Sally might win the second place and then on another day Sean might win the first place and Sally might win the second place. So everyday that you run this marathon assuming all these people are similar skill levels, some person is going to win first place and some person is going to win second place. So what we want to figure out is of the four people, how many different ways can that happen? How many different permutations are there because in this problem the order does matter, first and second place. It obviously matters what order these people come in. That is what a permutation is. I am trying to repeat it so you get the idea here.
So what are we going to do is instead of just trying to sit on you paper and you just try to make up all the different permutations there are, I mean you could go through this list and you could do your best to write the number of ways it can happen. The best to do this and what you will see in your book is to use what called a tree diagram. A tree diagram, you will see it looks like tree and it really helps you just map it out and so you make sure you do not miss anything. So what we are going to have is first we are going to say we are going to work methodically through this list and we are going to make sure we cover all the different ways this can happen. So let us say in first place, we have Jason because that is me right? I am Jason and I won as I am making the video all right?
So if Jason wins first place then obviously he cannot win second place so if Jason wins first place, he is not going to be for this particular solution, he is not going to be the second place winner. The only second place people are going to be these leftover people. So we are going to work methodically through it. Let us say that Sean wins the second place and this would be one permutation Jason and Sean. But on another day, Jason might have gotten first place and Sally might have gotten second place. And on another day Jason might have gotten first place and Martha might have gotten second place. So we have worked our way through several of these ways that it can happen. Jason and Sean is one day, Jason and Sally, Jason and Martha. Now let us continue one so I won first place and these guys were laying out here. Let us continue, let us say Sean won first place.
You can see why it is called the tree diagram. I am kind of building a tree here. So if Sean w
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