MediumProbabilitypr-124

1D Random Walk Return Probability

Problem

Probability that a symmetric simple random walk on the integers is back at the origin after 2n steps:

P(return) = C(2n, n) / 4^n.

Return 0.0 for negative n.

Hint

The walk must take exactly n steps right and n steps left.

case 1

in: [0]

expected: 1

case 2

in: [1]

expected: 0.5

case 3

in: [2]

expected: 0.375

case 4

in: [10]

expected: 0.17619705200195312

Starter codePython

import math


def random_walk_return_probability_1d(n):
    # Your code here
    pass

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