Question

Imagine you have m distinct baskets in which you’re throwing n number of balls at random. Each throw is independent of any other throw, and every basket is equally as likely to get a ball on a throw. After the n throws, what is the probability that a given basket is empty?

Answer 1

Answer:

$(\frac{m-1}{m})^n$

Step-by-step explanation:

Given a basket, the probability of a ball to end there is $\frac{1}{m}$ (because there are m baskets).

Then, the probability of a ball to end in other basket is $\frac{m-1}{m}$.

Finally, the probability of the basket to remain empty after n throws is

$(\frac{m-1}{m})^n$

This last is because, given n independets events with probability p, the probability for all of them to happen is $p^n$. In this case $p=\frac{m-1}{m}$