Expected Empty Bins

Problem

Expected number of empty bins after balls are thrown independently and uniformly into bins:

E[empty] = bins * (1 - 1 / bins)^balls.

Use linearity of expectation over bins. Return 0.0 for bins <= 0 or balls < 0.

Hint

Each fixed bin stays empty with probability (1 - 1 / bins)^balls.

case 1

in: [10,10]

expected: 3.486784401000001

case 2

in: [0,5]

expected: 5

case 3

in: [5,5]

expected: 1.6384000000000003

case 4

in: [3,0]

expected: 0

Starter codePython

def expected_empty_bins(balls, bins):
    # Your code here
    pass

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