Birthday Exactly One Shared Birthday

Problem

Poisson approximation for the probability of exactly one shared birthday among n people when days birthdays are equally likely. Treat the number of colliding pairs as Poisson with mean lambda = n * (n - 1) / (2 * days) and return lambda * exp(-lambda). Return 0.0 for n < 2 or days <= 0.

Hint

With lambda colliding pairs on average, exactly one pair occurs with probability lambda * exp(-lambda).

Test cases

case 1

in: [23,365]

expected: 0.3465741279391074

case 2

in: [2,365]

expected: 0.002732230201635231

case 3

in: [57,365]

expected: 0.05517505581177928

case 4

in: [10,365]

expected: 0.1089874506486353

case 5

in: [1,365]

expected: 0

Starter codePython

import math


def birthday_exactly_one_collision(n, days):
    # Your code here
    pass

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