 two, one, two, they could go up to 12, right? Because it's possible that I have some that had actually 12 successes, but unlikely that we flip the coin 12 times, but possible, right? So we got 12 up to here and then you would let's make this black and white hometown font group black, white, center, it's rapid and center it. Okay, I didn't mean to center it that way. Let's center it back to the okay. So so now we could say you would think you could use the count if equals count if and then brackets and you'd say well this range the outcomes I have control shift down. I'm holding control backspace comma and that's the criteria close it up, enter, right? Meaning every time you find a zero over here, you put it over here, we actually had two times where there were zero, zero heads, which is out of 12 flips, right out of all these thousand flips that we did. So that's so interesting. But I think it's easier or it's more useful oftentimes or safer to use a frequency spill array, because sometimes for whatever reason, these numbers may not be exactly whole numbers or something like that. So sometimes it doesn't pick up all the numbers. So I'm going to use equals frequency tab. And then the data array is going to be here. I'm going to hold control shift on the keyboard and down. And then I'm holding control backspace to get back to the top comma, then the bends, I'm going to put my cursor here, control shift down. And there are the bends. And so I can just hit enter. And it spills them down, it goes a little bit far here. So I'm going to try to trim that last bit off, double clicking on it. I'm going to get rid of that, bring it back to 13. And there we have it. Now, let's put the total down below. And it should total up to 1000 here because we did this 1000 times we did a thousand 12 round flips of the coin. So this equals the sum. Or I can do it quickly by saying alt equals, I got to click off and then back on alt equals, enter comes out to 1000. So that makes me feel like okay, picked up all the numbers of these 1000 rounds of 12 flips that we had. And these are the results. So two times out of 1000, we didn't get any heads in a 12 flips of the coin. With one heads, one time, zero times, we got two out of 12 heads, 13 times three out of 1244 times four out of 12, 119 times. And again, you would expect that somewhere like six out of 12 would be kind of in the middle of all of all these 1000 flips of 12 flips, right? And so now let's take a percent of the total. Let's take this as a percent of the total. I'm going to format paint home tab format paint that here. And this will equal the two divided by the 1000. I'm going to select f4 to make that absolute. So I'm going to take each number divided by the total enter. Let's make it a percent home tab font group percentify it adding a couple decimals, and then double click the fill handle dragging it down or taking it down. I'm going to delete that bottom bit, because I don't want to take this divided by this I want it to instead sum up alt equals some boom. Okay, so now let's compare that and look at the difference between what was what was given by the binome formula. So I'm going to select fill filling that in. I got to turn my music back on. In the background, you can't hear the music. I'd be copyright if I but here we go. So then I'm going to say this is going to be equal to this minus the I don't work without the music man. I refuse to keep going. Okay, we'll subtract that out. Percentify home tab number group percentify. You better recognize you can't recognize unless you percentify. And then we're going to copy that down. And then I could copy that across. And so so now you can see kind of the differences of what we got over here on the likelihood, right, that we get zero, you know, out of the out of the 12 flips, right, when we actually ran the test point to versus point two point two nine that we get one out of 12 the likelihood, right? And then this came out to zero. And then getting two is 1.61 and 1.3. And you would you would expect then that if I did this experiment more times like 1000 I did it 1000 times if I did it infinite amount of times like the entire population that we'd imagine the entire but an infinite that we would come out to these numbers, right? But we're taking a finite sample. So so then the idea would be that this this then gives us pretty good, you know, predictive power about this scenario, which has an element of randomness in it. Let's go ahead and plot this one to so I'll select, I'll plot them together. I'll select these items here. And let's do it with a line chart insert charts. Let's do a line chart. And go that one, that's the percent of the total line chart. I'm going to go to my data and edit the x. I want to pick up my x's. So don't just do your own x's Excel. And then I'm going to add another one, add another data set so we can see the other data set, which is going to be the P of x data set. And so we can see the differences on a side by side. And we'll say, okay, pick those ones up, por favor, if you please. And then okay, and okay. And so there we have it. So it's pretty, you know, they're pretty close, right? There. So you would think that the binom.dis gives us some predictive power, of course, and this kind of situation. And in practical situations, this actually comes up all the time. So whenever we can break something down to a success or fail situation, and then get an idea of what the likelihood is for any one, one round that we're doing, like flipping the coins, like a sales call is a common example, right? So every time I call someone, it might not be 50% chance of success, it's probably going to be far lower than that. But but if I haven't a chance of success percent, then then it's either a win-lose situation, I can start to plot out and and and get some idea of the results. Alright, let's go ahead and make this blue. I'll make this a header, home tab font group, black, white, let's make this blue and bordered font group, border it, make it blue. If you don't have that blue, it's in here. You don't have to use that blue, but that's what I do. It's nice and kind of bright. It doesn't remind me of the horror days of having to write this down in a spreadsheet and not being able to read my own writing. And people are like, you didn't add it up right because you couldn't read your own number two. That two doesn't look right. It's like, whatever, dude. Why don't you use Excel for crying out loud? What are we doing around here? You can't add that up in your mind? No, I can't add it up in my head. I control shift down. We're going to say a home tab. That's why we have computers for crying out loud. Control shift down and we'll make this, sorry to share my traumas with you, but I'm just saying the blue doesn't trigger the nightmares quite as readily. So there we have it. Let's do a quick spell check on it and frequency. Okay, looks good.