New lower bounds are proven for P(H ≥ E[H]) in the hypergeometric distribution, including a simple bound of k/n when n ≥ 8k and a variance-based bound under additional conditions.
Pinelis,Best lower bound on the probability of a binomial exceeding its expectation, Statistics & Probability Letters179(2021) 109224
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On lower bounds for hypergeometric tails
New lower bounds are proven for P(H ≥ E[H]) in the hypergeometric distribution, including a simple bound of k/n when n ≥ 8k and a variance-based bound under additional conditions.