def _prob_no_occurrence(
sample_size,
subsample_size,
sample_freq,
num_subsamples
):
"""Compute the probability that an type with a given probability does not
occur in a subsample of given size drawn from a population of a given size.
"""
if sample_freq > sample_size - subsample_size:
return 0
else:
return binom(
sample_size-sample_freq,
subsample_size,
exact=True
) / num_subsamples
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