Lesson 11 - Binomial Distribution (Probability Tutor)

hi and welcome to this section of the probability and statistics tutor and in this section we're going to build on what we did in the last section dealing with probability distribution functions when we introduced that and we're going to in this section talk about our first real probability distribution called the binomial distribution okay so the binomial distribution when you read it for the first time it really sometimes can can can make you feel confused and make you feel like it's a really tough thing but the thing that you need to know is that it's really not a big deal okay what we learned in the last section is that a probability distribution function is just a really fancy big word and all it really means is that you know you have functions from algebra one you put a number in you get a number out well these probability distributions are functions so to speak that instead of just getting any old number out at any given value of your random variable X you have a probability of that of that variable actually occurring with that value that's what's happening here so this is a binomial distribution it's a specific type of distribution okay in the last section we were talking in general terms here's a probability distribution and I just write it down in a chart form or in a histogram form you know in a bar graph or something to kind of show you what it is we learned about it in this section we're gonna study a very specific very useful very common probability distribution called the binomial distribution so what we're gonna find for each of these problems really is that once you learn the way the problem is constructed and know that it's a binomial distribution what's going to happen every time is you're going to write down with your pencil you're going to write down an actual function f of X is equal to and you're gonna write down what this function is just like a you know a function form algebra one yeah or or trigonometry or something you know f of X is equal to x squared at one time that looked really foreign to you so here in the beginning with the binomial distribution it's gonna look a little foreign to you but once we tackle some problems and see how it's applied it's not a big deal it's actually not a big function at all so what we're gonna do is we're gonna write down this binomial distribution we're gonna learn how to calculate the values of the function at various values of X and we're also going to talk a little bit at the end about using the tables in the back of your book that that almost every book on statistics will have and teach you kind of how to use as well so most books will just start out by writing down what the binomial distribution is and telling you to learn it and love it and try to teach you how to do it I want to start out with an example because I feel that that's that that's the best thing to do so forget that we're learning about something complicated called a binomial distribution and just work with me on this example okay here's what I want you to think about let's say we have four questions on a test it's a multiple-choice test so there's question 1 question 2 question 3 question 4 I have no idea what this test is about okay because I didn't study so I'm gonna guess at this test each question has five choices a B C D and E right so it's actually something you might actually enjoy learning about anyway just for just for giggles because what I'm gonna end up asking you is what's the probability of getting some of these questions right and wrong okay and what's the probability of doing well and doing poorly on the test okay so four questions and each question has five choices okay so let me ask you this if you completely guess at any given question No forgive the fact that there's four questions on question number one if I completely guess at it and there's five choices what is the probability that I'm gonna get that question right five choices all right so learning from probability we know that there's only one way to get the right answer and there's five choices so the probability of getting a right answer is 1/5 right okay okay so the probability of guessing on one of these questions just the first one okay the probability of getting the right answer I'm gonna call that probability P okay just P so that's what I'm gonna call it and I'm gonna say that it's equal to 1/5 because we just said that at the probabilities 1/5 since there's 5 choices and we're gonna go and convert that to a decimal I think you can convince yourself you put that in a calculator you'll find out that the probability 0.2 okay 1/5 now what would be the probability of the wrong answer of guessing the wrong answer the probability of the wrong answer so again it's just question number 1 it's 1/5 that we got the right answer how many choices how many wrong choices are there there's for wrong choices in every single question right so the probability of getting the wrong answer is pretty high four-fifths because there's four ways to get the wrong answer and only five choices so instead of using P I've already used that thing so I'm gonna call him Q and we already said that the probability of Q getting the wrong answer is a is 4/5 but we also know that Q is equal to one minus P and we know that it's equal to 4/5 because we just said it's equal to 4/5 in other words if the probability of the right answer is 1/5 then the probability of the wrong answer is just 1 minus the probability of the right answer and we've been doing this this 1 minus business ever since the beginning of the probability so that should not look foreign to you okay if it is go back and review that now so probability a right probability of a wrong and so you would guess this is 0.8 1 minus 0.2 0.8 right so far it hasn't been rocket science so for for one question the first one on the test 1/5 of being right 4/5 of being wrong okay now the question I'm going to ask you and actually the form of all of these binomial distribution things we're going to learn about the form of the questions always going to be like this what is the total probability for this particular problem of guessing three out of four of the right answers of their other questions correctly so four questions one two three four we know what the probability of getting the questions right and wrong is of each individual question but now that there's four questions we just want to calculate what's the total probability that

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Length: 6min 0sec (360 seconds)

Published: Thu Aug 18 2016