Pass@k Unbiased Estimator

Problem

Given n sampled completions, c correct ones, and k draws, return the unbiased pass@k estimate 1 - C(n-c, k) / C(n, k), where C is the binomial coefficient. Return 0.0 when n <= 0, k <= 0, or c <= 0, and 1.0 when k >= n or n - c < k.

Hint

C(n-c, k) is zero whenever k exceeds n - c.

Test cases

case 1

in: [10,2,5]

expected: 0.7777777777777778

case 2

in: [5,1,1]

expected: 0.19999999999999996

case 3

in: [5,0,3]

expected: 0

case 4

in: [4,4,2]

expected: 1

case 5

in: [6,3,2]

expected: 0.8

Starter codePython

import math
def pass_at_k(n, c, k):
    # Your code here
    pass

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