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Here is an example of a tiny Bloom filter. It uses an array of 8 bits and two independent hash functions fand 9. We want

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Here is an example of a tiny Bloom filter. It uses an array of 8 bits and two independent hash functions fand 9. We want to test membership in a set S of three elements, so we hash each of the three elements using both fand g, and we set to 1 any bit that any of the three elements is hashed to by either of the hash functions. When a new element x arrives, we compute f(x) and g(x), and we say x is in the set S if both f(x) and g(x) are 1. Assume x is not in the set S. What is the probability of a false positive; i.e., the probability of saying that x is in 8. provide explanation

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