Bonferroni Intersection Lower Bound

Problem

Bonferroni's inequality lower-bounds the probability that all events occur: P(intersection) >= sum(probabilities) - (number of events - 1), truncated below at 0. Return the bound, which is 1.0 for an empty list.

Hint

The complement of the intersection is bounded by the sum of the complement probabilities.

Test cases

case 1

in: [[0.9,0.8,0.7]]

expected: 0.40000000000000036

case 2

in: [[0.5,0.5]]

expected: 0

case 3

in: [[0.99,0.99,0.99,0.99,0.99]]

expected: 0.9500000000000002

case 4

in: [[]]

expected: 1

case 5

in: [[0.2,0.3]]

expected: 0

Starter codePython

def bonferroni_intersection_bound(probs):
    # Your code here
    pass

5 test cases · run your code against them in the editor