this video is fairly long so if you'd like to skip ahead to any of the portions of this example please click on the appropriate link now okay I'm going to show you how to use your ti84 calculator to calculate binomial probabilities now this this is a very very useful functioning the calculator and it's kind of intuitive as long as you understand the format that you need to be able to put everything in now one problem that a lot of students uh find when using the binomial function in their calculator is that there are actually two different functions there's the Bome PDF and Bome CDF now the one with the p that is going to be when you were looking for a very specific random variable okay so when you're looking for a specific amount of successes and the one with a C stands the C stands for continuous is when you are looking for a range of successes okay so the way you have to put things into the calculator for the bom PDF is you always first put the total number of Trials the probability of a success and then the value that you're trying to look for okay um with bom CDF you the first two um options are the same but the last option is the value that X has to be less than or equal to now this is really important and this can be something um that can make you accidentally enter it into your calculator and CCT me and I'll show you some examples uh while we do this so you can see how it works now um let's see so let's look at an example now first I want to say that this statistic is completely made up for this example I have no idea what percentage of college student college students actually drink alcohol but anyways 70% of college students drink alcohol you randomly select 13 college students and ask if each if he or she drinks alcohol find the probability that the number who say they drink alcohol is exactly 10 notice this is looking for exactly so we want to know um what the probability that 10 of the 13 students that we speak to say they do drink alcohol so what we're looking for here is P that X is equal to 10 okay now because this isn't exactly then we will be using um the binom PDF function here okay so I'm going to write out exactly what I need to do I need to do 13 because there are 13 total trials the probability of a success is 70 because 70% drink alcohol and the amount of successes that we are looking for is 10 okay so I just put that in my calculator now the way I get this is I hit the second key and then V RS vars and that notice gives me distribution distribution so if we go down um all the way or the easier way to do it is press up you press up oops too many times Bome PDF enter okay so we're going to do 137 and 10 so the probability is 218 approximately okay well this time we want to know if um it is exactly 13 okay so this time we're looking for the P that X is equal to 13 now I'm not going to write the function but it's essentially the same except instead of a 10 here we're going to go 13 now what you can do to save yourself some time instead of having to key all that stuff again in again is to do second and then hit the enter key that brings up entry it'll bring up the last thing that you typed well all you have to do is go and change that zero to a three and voila it's approximately. 9 69 okay once we start getting to these ranges is when you have alternate ways or different ways of solving them and when it get a little kind of confusing I'm going to first do this one in um one way and then the one further down that's also an at least problem I'm going to do it in a different way so you can see the two different ways to do it okay now the probability that it's at least 11 is the probability that X is greater than or equal to 11 okay now what I can do is I can actually break this up into three separate probabilities I can do it that probability that X is equal to 11 and you don't have to write this x equals you can just write um P of 11 and probability that X is equal to 12 plus the probability that X is equal to 13 okay so we can do uh this by just saying well if it's greater than or equal to 11 that means it needs to be 11 or 12 or 13 okay and in probabilities whenever you have the word or you represent it with a plus and that's supposed to be quote it looks kind of weird my pen messed it up anyways so these are all bom PDFs that we can just do now I'm going to do this all in one swoop um make this a little easier for myself I'm going to do bom PDF change this to an 11 then plus can keep doing this oops actually I can't do that 11 plus let's just go ahead and do it oh I keep hitting it too many times I on PDF now be very careful that you don't accidentally do the CDF one because if you do you're going to not going uh you're not going to get the correct answer because it is a completely different function okay so what I did was I just did all three of them um where everything is the same except for the third number okay the 11 for X = to 11 the 12 for x = 12 and the 13 for x = 13 let me make sure I got everything else right Point yeah okay Enter so the probability that at least 11 of them said that they drink alcohol is202 okay now I'm going to show you how to do one like this um down in example e using the CDF function it's much easier okay well D is asking that um the probability that less than four say that they drink alcohol so p x is less than four now the problem with the PDF function is that if you want to do a range like this you have to add a whole bunch of them together so this is why the CDF function is really helpful because it will calculate a range however it will only do a range if the last value you put in is less than or equal to what you're looking for X to be so in this case this is no this is not or equal to it's just less than so what I want to do is rewrite it in the form less than or equal to so because this is um because these are not continuous data values um because they're discret there is actually a gap between them so that means that for X to be less than 4 that means X has to be equal to 0 1 2 or 3 or X is less than or equal to 3 okay so now I have it written as a less than or equal to so what I want to do is use the Bome CDF okay now it's still going to be 13.7 because that's the number of Trials and the probability of it's sucess and then this number needs to be the number that X is less than or equal to 3 now this is the reason right here why I rewrote it because in this format it's not exactly obvious that the last number needs to be a three it makes it look like it needs to be a four okay so now all I need to do is put this in my calculator so go to distribution and I think you can just hit oh see calculator being silly right now okay V sorry supposed to be vom CDF see make sure that you use the correct function enter okay find on CDF we do 13.7 three okay so this says um 6.51 96 and this E4 means * 104 whenever you get a um negative here the easiest way to do it is just say well there's going to be a point and then some amount of zeros and then all this stuff here well the amount of zer is always going to be one less than whatever this number is here so um we just do 0 0 three zeros and then we can just write the rest of it 65 2 okay so if that was e to the5 you would do 4 zeros if it was e to -10 you would do 9 zeros okay so that's the easiest way to deal with negative scientific notation which you will get a lot in um probability okay all right the next one is at least four now I told you back in C that I would show you an easier way to do this and the easier way to do this is to use the complement rule so the probability that X is greater than or equal to 4 is going to be 1 minus its complement okay now the complement because this is a greater than or equal to its complement will be a less than or equal to and the less than or equal to is the way the binome uh the binome CDF function in the calculator needs to be used so what we'll do is we'll say well this is the probability um 1 minus the probability that the complement of this so this is uh four and up so what we want is three and down so X is less than or equal to three those would be the other options okay now um you could have also said this is the same thing as p is of X is less than 4 okay so same thing that we found before so it's just going to be 1us the 00652 that we found in the previous one um so one and I'm going to just use the answer in the calculator have it do it so 9 9 9 now what I also could have done is done um one minus and then put in the Bome CDF function okay which was part of the reason for writing it like this all right the next one is at most four so this is the probability that X is less than or equal to 4 now this one's easy it's just the um binom CDF so um let's do go back a few times okay and change that three to a four so 0 0 43 and the last one is the probability that it's more than four okay so this probability that X is greater than 4 okay now this one the easiest way to do it is to once again use the complement rule so we're going to do one minus the probability of its complement now its complement would be um if this is 5 6 7 8 9 all the way up 3 13 this would be four and down so X is less than or equal to 4 okay now we found that in the previous one but I'm going to show you how to do it in the calculator we can just do 1 minus bom CDF of 13.7 and 4 okay so we could either just do one minus the amount we found in F or we can do one minus so this is equal to9 9 six okay so the big thing to remember when working with the binom PDF and bom CDF function is that the binome PDF is for exact values there is no range when you're looking for the binom PDF with the CDF you're looking for range and the number that goes in the third spot needs to be the highest possible value that you're looking for okay so if you have these open intervals like in e and G you need to convert it so that the number that you're going to put into calc into the calculator will be the largest possible value that you're looking for