 actually help for some memorization tools if you had a system like that coming up as well. Then I can say, okay, well, how can I simulate possibly a random draw from a deck? So this is how you can kind of make a computer, your own little computer card game or something, right? You can program basically Excel into some degree. You can say, well, what if I took a random draw of 52 cards? Well, I can use the random generator here now because I've named each card individually, the bottom card being one, the top card being 52. Now notice there's kind of an issue with this. I won't get into it right now if you were to try to play games with this or something like that, because if you took one card out of the 52 card deck, right, now there's only 51 cards and that one card you took out is gone. So you have to kind of account for the fact that when you draw cards out in a practice game. But I won't get into that in detail here. Just want to note that you can kind of create a generator here based on this now by saying I'm gonna make a random generator and here's my random generations as if I took one card, I put it back in the deck, shuffled the deck again and drew one card and each of these numbers then represent a unique card because according to my table. So the first one I drew 39, 39 according to my table is the 13 of diamonds which is a king of diamonds because 13 represents a king. Cause it comes from, right? So then if I had a 48, 48 represents the nine of clubs, okay? So now we've got a unique card and I could even take these numbers if I wanted to and tell Excel to find the related suit. So it'll give me the number and suit but we won't get into that now. But then I can take my random numbers from my random number generator which is always just gonna keep generating random numbers and then paste it so that it's just a hard coded number over here. So now I've pasted these random numbers that we drew out and we can do some analysis of it. So let's take a look at our table here. Let's do it this way. So this is a similar table that we had before where we had our aside numbers. So these are the aside numbers. These are the card numbers, one through 13 spades, one through 13 hearts, one through 13 diamonds. These are the numbers we assigned just one through 52. These are the suits and then we have, that's just deleted here, we have the results. So the results are using this count formula which I'm saying we're telling Excel count this range of data if the range of data has the assigned number in it. So in other words, this cell has this formula in it which is using account function. And we wanna say, given this sample that we just drew out a number every time we drew a number out of the deck and then put it back into the deck, right? And then drew out another number, one out of 52 each time of the random sample. However, many times we did it, we did it a fair amount of times is gonna give us a 79. So 79 times it was an ace, an ace of spades particularly, right? And then 100 times it was a two. And then notice down here, if I go down here, this is a 29, so it looked for how many 29s I got and the 29s represent a three of diamonds. So we had 88 three of diamonds, you see that are drawing out of here. Now, if I look at the percentage then, this then is the percent compared to the total. So if I add up all the results, the results add up to 5,000. So we actually did this 5,000 times. So we kind of mimicked us taking a card out of the deck and then putting it back into the deck, shuffling it, taking a card out, you know, 5,000 times. All right, and then so the total of these is 79, 79 over 5,000. If I move the decimal two places over, that's 1.58. So that means we drew out an ace of spades 1.58% of the time. This one is 100 divided by 5,000. So that's 2%. So we drew out 2% of the time, a two of spades. So three of spades, we drew out 109 over 5,000 which is 2.18%. Now, according to what we would expect to happen because we're kind of mirroring a similar situation with the coin flip here, where in the coin flip, we kind of imagined that the entire population would be as though you did this infinite amount of times, in which case, if it was a fair coin, it would be 50 head, 50% head, 50% tail. And this case, same kind of concept, we would say, well, if we imagined that we did this infinite amount of times, drew a card out of the deck and then put it back in, drew a card out, an infinite amount of times, then we would expect that it would come out to be one over 52, which is gonna be that 0.92, if I move the decimal place over percent, about, rounded. So now we can compare our results, the statistical results. We came up with 1.58, 79 times out of 5,000 versus the actual, so we have our differences of, in this case, 0.34, 0.08, and you can see that the differences are gonna summer over and summer under. So we have a similar kind of situation we did with the coin flips here, right? With the coin flips, we were trying to, the null hypothesis was the coin was fair and we want to then flip the coin multiple times to see if that was false. Same thing here, the null hypothesis is that the deck has 52 cards in it and it's fair and you're drawing it correctly and it's a random draw and all that kind of stuff. And if that was the case, we would expect, if you did it infinite amount of times, it would come out to 1.92, and so then we're gonna do it and see if that is the case and with our statistical analysis and this is our differences that we have here. So then if I summed up all of the, if I averaged all of these numbers, I come up to 1.923, which is pretty close to the actual result, right? Because we did it a fair amount of times. And by that, I mean we ran the experiment a lot of times, 5,000 is pretty a good number of times. So now we could also say, well, what if I took, what if I took the count of the spades, for example, because we know with the statistical numbers that we looked at, we'd say, well, if I just looked at spades, there's 13 out of 52. So if I did that infinite amount of times, if I drew one card infinite amount of times, you would think that I would have a spade like 25% of the time, right? So then if I count the spades here, that's gonna be using this formula. So now I'm looking for the spades. So just notice the function here, you could arrange this function a couple different ways, because now I've got a sums if function, meaning I want you to sum the results, so the results are gonna be this column, and I want you to sum them for the spades. So here are all the spades down to here. Now, in order to sum the spades, I could tell, Excel, I want you to sum this column, the sum range, if this column has a spade in it, right? That would be the easiest, that's probably...