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What is the expected error for estimating the Jaccard index using MinHash scheme for k different hash functions?

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What is the expected error for estimating the Jaccard index using MinHash scheme for k different hash functions?

(a) O (log k!)

(b) O (k!)

(c) O (k^2)

(d) O (1/k½)

My query is from Hash Tables topic in portion Hash Tables of Data Structures & Algorithms I

I got this question by my school teacher while I was bunking the class.

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Best answer
Right option is (d) O (1/k½)

Best explanation: Jaccard Coefficient Index is defined as the ratio of total elements of intersection and union of two sets. For two disjoint sets, the value of the Jaccard index is zero. The expected error for estimating the Jaccard index using MinHash scheme for k different hash functions is O (1/k½).

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