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Current time:0:00Total duration:6:55

CCSS.Math:

there's a lot of times there's a lot of situations in which we're studying something pretty straightforward and we can find an exact theoretical probability so what am I talking about let me write that down theoretical theoretical probability well maybe the simplest example or one of the simplest examples is if you're flipping a coin and let's say in theory you're flipping a completely fair coin and you're you're flipping it in a way that is completely fair well there you know you have two outcomes the coin will either result either heads will be on top or head tails will be on top and so theoretically you say well look if I want to figure out the probability of getting a heads in theory I have two equally likely possibilities and heads is one of those two equally likely possibilities so you have a 1/2 probability and once again if in theory the coin is definitely fair it's a fair coin and it's flipped in a very fair way then this is true you have a 1/2 [ __ ] you have a 1/2 probability we could also do that with rolling a die a fair six-sided die is going to have six possible outcomes one two three four five and six and if you said what is the probability of rolling a or getting a result that is greater than or equal to three well we have six equally likely possibilities you see them there and in theory if once again if they're all equally likely four of these possibilities meet our constraint of being greater than or equal to three so we have four out of the six equal of these possibilities meet our constraints so we have a two-thirds four six is the same thing as 2/3 probability of it happening now these are for simple things like die or flipping a coin and if you have fancy computers or spreadsheets you can even say hey I'm going to flip a coin a bunch of times and do all the competent orcs and all that but there are things that are even beyond what what a computer can find the exact theoretical probability let's say you're playing a game say say football American football and you wanted to figure out the probability of scoring a certain number of points well that isn't very simple because that's going to involve what human beings are doing minds are very predictable how people will respond to things the weather might get involved there might be someone might fall sick the ball might be wet or you know just how the ball might interact with some players the jersey who knows what actually might might might might actually result in the score being a one you know one point this way or seven points this way or seven points that way and so for situations like that it makes more sense to think more in terms of experimental probability an experimental probability we're really just trying to get an estimate of something happening based on data and experience that we've had in the past so for example let's say that you had this is you social this is data from your football team and since it's a couple of games or many games into the season and you've been tabulating the number of points you have a histogram of the number of games that scored between 0 9 points your two games it scored between 0 9 points for games that scored between 10 and 19 points included or 10 from 10 to 19 points you have 5 games that went from 20 to 29 points you had three games that went from 30 to 39 points and then you had two games that go to from 40 to 49 points now let's say for your next game and let's say you've already had two let's see how many games you've had so far this is to let me write it down the game so far is two plus four plus five plus three plus two so this is what six plus this is 6 plus 5 is 11 11 plus 5 is 16 so you've had 16 games so far this season and you're curious for your 17th games let me write this game game 17 you want to figure out what is the probability of scoring scoring scoring let's say score let's say your score let's say your points your points are greater than or equal to 30 your points are greater than or equal to 30 for game 17 so once again this is very hard to find the exact theoretical probability you don't know exactly you can't predict the future you don't know who's going to show up sick how humans are going to inter with each other maybe someone screamed something in the stand that just phases the quarterback and exactly the right or the wrong way you don't know this is incredibly incredibly complex system how what might happen over the course of an entire football game but you can estimate what will happen based on what you'll see in your past experience and it depends on the defense of the team you're facing and all that so it's not going to be you know it's not going to be super exact but you can estimate based on experiments based on what you've seen in the past here the experimental probability and I would say the probability the estimate because I would I don't you know don't you you shouldn't walk away saying this okay we absolutely know for sure that if we conducted this next game experiment end times it's definitely going to turn out the same thing this might be the toughest gate defense that you play all year this might be the easiest defense that you play all year but if you look at what's happened in the past out of the 16 games so far there have been three games these three plus these two games where you scored more than greater than or equal to 30 points so five out of the sixteen situations you scored more than that so an estimate of your probability and then you could view this as your experimental probability of scoring more than thirty points based on past experience based on past experience is five five out of the sixteen games you've done this in the past so you'd say it's five sixteen now I want to really have you take this with a grain of salt you should not you know then go good say okay I know for sure there's a 5/16 probability of us winning this game because you only have some data points every team you play is going to be different it's going to be different weather conditions people are going to be in different moods etc etc this is really just an estimate I actually I I feel even a little bit of reservations even calling it a probability I would just say that this has been true of five out of 16 games in the past so it's an indicator of what might what might be what you know you might say okay no based on experience it's more likely than not that we don't score more than thirty points but it's really just based on experiential data what's happened in the season you know even the makeup of your football team might have changed you might have gotten a different coach you might have learned to train better who knows one of your team members might have grown by 3 inches all of these things so all of this has to be taken with a grain of salt but this is one way of thinking about at least having a sense of what may happen