MediumProbabilitypr-167

Probability of At Least One Fixed Point

Problem

Probability that a uniformly random permutation of n items has at least one fixed point:

P = 1 - D(n) / n!

where D(n) is the derangement count. The value approaches 1 - 1 / e. Return 0.0 for n <= 0.

Hint

Complement of the hat-check no-match probability.

case 1

in: [1]

expected: 1

case 2

in: [2]

expected: 0.5

case 3

in: [3]

expected: 0.6666666666666667

case 4

in: [4]

expected: 0.625

Starter codePython

import math


def probability_at_least_one_fixed_point(n):
    # Your code here
    pass

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