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93237a0 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 | from fractions import Fraction
prior = Fraction(1, 50)
sensitivity = Fraction(19, 20)
false_positive = Fraction(1, 10)
def posterior(positives):
good_evidence = prior * sensitivity ** positives
other_evidence = (1 - prior) * false_positive ** positives
return good_evidence / (good_evidence + other_evidence)
one, two = posterior(1), posterior(2)
assert 0 < one < two < 1
result = {"one_positive": str(one), "two_positives": str(two)}
import json
print(json.dumps(result, ensure_ascii=False, sort_keys=True))
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