Hat-Check No-Match Probability

Problem

Probability that in a random permutation of n hats no one gets their own hat back:

P = sum from k = 0 to n of (-1)^k / k!

which converges to 1 / e. Return 0.0 for negative n.

Hint

This is the derangement probability, the inclusion-exclusion complement of all match patterns.

case 1

in: [0]

expected: 1

case 2

in: [1]

expected: 0

case 3

in: [3]

expected: 0.33333333333333337

case 4

in: [10]

expected: 0.3678794642857144

Starter codePython

import math


def hat_check_no_match_probability(n):
    # Your code here
    pass

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