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

`((m-1)/(m))^n`

Explanation:

Given a basket, the probability of a ball to end there is
`(1)/(m)` (because there are m baskets).

Then, the probability of a ball to end in other basket is
`(m-1)/(m)`.

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

`((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=(m-1)/(m)`