A total of $n$ balls are thrown to $m$ urns, each urn has the same probability of catching a ball. What is the probability that the $n$th urn is empty?
What i've tried:
i figured the probability of any ball to fall inside an urn is $\frac{1}{m}$. Based on that, I tried to propose a binomial distribution:
$$\sum_{x=0}^n {n \choose x}\left(1-\frac{1}{m}\right)^x \left(\frac{1}{m}\right)^{n-x}$$
but i'm not sure if this is correct
You have correctly figured out that the probability of a ball to land in a particular bin is $$p=\frac1m .$$
Thus the probability that all $n $ balls land in other bins is $$(1-p)^n. $$