 The cell has a two in it. So here's the criteria count if that range has the criteria of a two and then it counted how many of them there are and then we divided we divide out to get to our Heads which is the heads divided by the total next we might want to run similar Examples or experiments where we're going to flip it more times So in this case our number sequence got a little bit messed up over here in excel But we're imagining these are multiple tests where we're going to be flipping the coin many more times using the same concept in Excel of equals random between one and two one representing heads to representing tails So now we have a bunch of tests that we did and we just copied this random Generation tool in all of the cells. This is just gonna randomly generate All of our outcomes for us and then if I copy that entire random generation Tool on to another cell so that I can then change it from a random generation To just hard-coded numbers we get our results And so again the number sequence on the left hand side got a little bit messed up So we we we've flipped it a bunch of times here. I'm not sure exactly how many times But we will find out in the calculations down here So then I can sum each of these up So if I look at the heads the formula is going to be excel look at this column of numbers that we flipped I think it's going to be 75 times but look at that column of numbers and Then and then tell me how many times count the times that you see a one and and excel gives us 34 times and then we do the same thing for the tails we say hey excel Count this column of numbers and tell me how many times you get a 41 and I mean, I'm sorry how many times you get a 2 that's this count if and excel says 41 times Now between a 1 and a 2 which are the two things that populate these cells we come up to 75 as the total And so then we can say alright if there's 75 of them. I can take a look at the heads 34 out of divided by the tails I mean divided by the total 75 and that comes out to 45 about percent 45 point 33 percent I could do the same for the tails 41 divided to buy out of the total 75 gives us 54 point six six fifty five about 45 plus 55 is a hundred percent which is kind of our double check that we have done things Correctly there so then if I if I look at it just the heads then I would expect it to come out You know 50-50 or the entire population if it was a fair coin would be 50-50 if we flipped it infinite amount of times Here we came out to 45. There's 53 56 52 We could do the same thing for tails of course But if we just zero in on one of the outcomes then it gets a little bit easier for us to think of that Series of outcomes right so 60 this one's you know pretty high kind of outline for 74 flips, right? But it still could clearly happen that we have you know 45 Here's our you know, it should be you know, we would think it'd be around 50 50 now if I took that series here of Percentages results. I might want to extract that and put it in a vertical Column in a column format so I could do that so I could in Excel. I could do that by basically Copying it and then pasting it and Transpose it so we'll do that in Excel if you want to practice that in this practice problem in Excel And then I could compare it to what the hypothetical Expected result would be meaning this would be the average For the entire population it would come out 50 50 if we flipped it infinite amount of times if it was a fair coin and then we can look at the differences between The outcomes per test so this is the outcomes per test 45 percent heads versus 50 percent for the actual This one came out 53 versus three Versus 50 3 percent difference 56 versus 50 and you could see that of course We would expect that some of some of the outcomes would be over some would be under If these were random samples now if we counted all of the tests which we did 75 of them Then and if I took the average of all the averages Then we're getting pretty close right now We're at 50.33 as opposed to 50 so so so you could see as of course We take a larger sample you would expect us to get closer to the actual average Of the entire population which is a theoretical concept in this case of 50 50 of an infinite number of flips so here's the the the number of heads if we were to take a a Histogram of the data and so and then this one So let's look so we could do and we could do this multiple times right I could take the random number generator and Basically do the same The same thing again, and we're not going to come out with the exact same results. You'll see over here We came out with well, I can see it in my data the first one was was 45 percent and over here Where did I where did I just go I came out with? 45 Well that one happened to be the same but then it was 53 and 56 So if I go back on over so now we did the same thing and I've got I've got The 45 51 51 so here's the same process that we did to generate another bunch of flips 75 flips each and And we did it, you know multiple times we could take the same, you know data the heads data Represented vertically so here it is represented vertically 45 51 51 and we can compare you know histograms That are generated from them the histograms Are not going to be you know exactly the same but you would expect them to start Looking similar as we have You know larger data sets would be the general idea So these are histograms of the averages of all the outcomes that we did a hundred tests of 75 now then you might then say well well, how could I simulate a Situation where it's not a fair coin. So now I now I have the null hypothesis