Why are two draws without replacement from an urn not independent?

In probability theory, two events are considered independent if the occurrence of one does not change the probability of the other. Drawing two balls from an urn without replacement is not independent because the outcome of the first draw alters the composition of the urn for the second draw.12

For an urn containing $r$ red balls and $b$ black balls, the probability of drawing a red ball on the first attempt is $\frac{r}{r+b}$. If a red ball is removed, the urn then contains $r-1$ red balls and a total of $r+b-1$ balls. Consequently, the conditional probability of drawing a red ball on the second attempt becomes $\frac{r-1}{r+b-1}$. Because this probability differs from the initial probability, the second draw is dependent on the first.23