Broken Bloom Filters

A bloom filter is composed of a bit array of 2162^{16} bits. We are told that the filter is designed to be optimally performing when there are 282^8 entries.

Given that the filter is filled with 282^8 entries, what is the expected number of queries one has to perform to perform to get a false positive?

If your answer is xx, enter the value of log10x\lfloor \log_{10} x \rfloor.

Notation: \lfloor \cdot \rfloor denotes the floor function.

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