So you'd feel pretty good that the independence condition is met. And once again, this is valuable when you are sampling without replacement. Now to appreciate how our confidence intervals don't do what we think they're going to do when any of these things are broken, and I'll focus on these latter two, the random sample condition. That's super important, frankly, in all of statistics. So let's first look at a situation where our independence condition breaks down. So right over here, you can see that we are using our little gumball simulation. And in that gumball simulation, we have a true population proportion, but someone doing these samples might not know that.