k-out-of-n Reliability

Problem

Reliability of a k-out-of-n system of identical components, each working independently with probability r:

R = sum from i = k to n of C(n, i) * r^i * (1 - r)^(n - i).

Return 0.0 for invalid parameters.

Hint

The number of working components is Binomial(n, r); sum the upper tail.

case 1

in: [3,2,0.9]

expected: 0.9720000000000001

case 2

in: [3,1,0.5]

expected: 0.875

case 3

in: [1,1,0.3]

expected: 0.3

case 4

in: [3,4,0.5]

expected: 0

case 5

in: [2,0,0.4]

expected: 1

Starter codePython

import math


def k_out_of_n_reliability(n, k, r):
    # Your code here
    pass

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