Now, with that out of the way, let's make ourselves feel good about this mathematically, and we're gonna leverage some of our expected value properties. In particular, we're gonna leverage the fact that if I have the expected value of the sum of two independent random variables, let's say x plus y, it's going to be equal to the expected value of x plus the expected value of y that we talk about in other videos. And so, assuming this right over here, let's construct a new random variable. Let's call our random variable y. And we know the following things about y. The probability that y is equal to one is equal to p, and the probability that y is equal to zero is equal to one minus p. And these are the only two outcomes for this random variable. And so, you might be seeing where this is going.