Exercise $4\mathrm{.}3\mathrm{.}2$: Suppose we have n bits of memory available, and our set S has m members. Instead of using k hash functions, we could divide the n bits into k arrays, and hash once to each array. As a function of n$,$ m$,$ and k$,$ what is the probability of a false positive? How does it compare with using k hash functions into a single array? The question is from Mining Massive Datasets, Chapter $4$ Section $3$ on Bloom Filtering. The formula for $1$ array into k hash function is given by $(1-e^{-\frac{km}{n}}$