Question

Suppose that we throw balls into m bins until some bin contains two balls. Each throw is independent, and each ball is equally likely to end up in any bin. What is the expected number of ball throwed?

Answer 1

The formula for all b bins having at most 1 ball after k tossings that you wrote is:

`((b)k)/(b^(k) )\\`

So the probability that at least one collision occurs in k throwings (that at least one bin will contain at least two balls) is:

`1-((b)_k)/(b^k)`