Monty Hall Switch Win Probability

Problem

In the Monty Hall game you pick one of n_doors doors, the host opens a different door with no prize, and you switch to one of the remaining n - 2 unopened doors. Return the probability that switching wins:

P = (n - 1) / (n * (n - 2)).

Return 0.0 when n_doors < 3, since there is nothing to switch to.

Hint

Your first pick wins with probability 1 / n, and the prize is behind all other unopened doors otherwise.

Test cases

case 1

in: [3]

expected: 0.6666666666666666

case 2

in: [4]

expected: 0.375

case 3

in: [5]

expected: 0.26666666666666666

case 4

in: [2]

expected: 0

Starter codePython

def monty_hall_switch_win(n_doors):
    # Your code here
    pass

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