### Lemma

[1] Consider a process that throws balls uniformly at random into b bins and let C be a subset of these bins. If the process throws balls, then the probability that each bin in C has at least one ball is at most if , where is some constant strictly less than 1. If , then the probability is at most .

Comment: conpon analysis + chernoff bound

### Lemma

[1] Consider a process that throws t balls into b bins uniformly at random. if , then the probability that there are at most occupied bins is at most .

### Lemma

[1] Consider a process that throws balls uniformly at random into b bins and let C be a subset of these bins. If the process throws q balls, then the probability that at least of the bins in have at least one ball is at most if ; and at most if .

## Reference

[1] Co-Location-Resistant Clouds, by Yossi Azar et al. in CCSW 2014