Inclusion-Exclusion Four Events

Problem

Inclusion-exclusion probability of the union of four events.

Given singles (4 individual probabilities), pairs (6 pairwise intersections), triples (4 triple intersections) and p_all (the quadruple intersection), return the alternating sum: sum(singles) - sum(pairs) + sum(triples) - p_all.

Hint

The signs alternate by intersection size: plus, minus, plus, minus.

Test cases

case 1

in: [[0.3,0.4,0.2,0.1],[0.1,0.05,0.04,0.12,0.08,0.06],[0.02,0.01,0.03,0.02],0.005]

expected: 0.625

case 2

in: [[0.5,0.5,0.5,0.5],[0.25,0.25,0.25,0.25,0.25,0.25],[0.125,0.125,0.125,0.125],0.0625]

expected: 0.9375

case 3

in: [[0,0,0,0],[0,0,0,0,0,0],[0,0,0,0],0]

expected: 0

case 4

in: [[1,1,1,1],[1,1,1,1,1,1],[1,1,1,1],1]

expected: 1

case 5

in: [[0.1,0.2,0.3,0.4],[0,0,0,0,0,0],[0,0,0,0],0]

expected: 1

Starter codePython

def inclusion_exclusion_four_events(singles, pairs, triples, p_all):
    # Your code here
    pass

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