My answer to 538's riddler at https://fivethirtyeight.com/features/the-little-mathematically-determined-house-on-the-prairie/

umbrella_riddler.py

#!/usr/bin/env python

import random

TRIES = 10000000
MORNING_RAIN_PROB = .5
EVENING_RAIN_PROB = .4

def is_raining(prob):
    return random.random() < prob

def simulate_week():
    home_count = 2
    work_count = 1
    for i in range(5):
        # Morning
        if is_raining(MORNING_RAIN_PROB):
            if home_count == 0:
                return False
            home_count -= 1
            work_count += 1
        # Afternoon
        if is_raining(EVENING_RAIN_PROB):
            if work_count == 0:
                return False
            work_count -= 1
            home_count += 1
    return True

n_dry = 0
for i in range(TRIES):
    if simulate_week():
        n_dry += 1

print("{} tries, {} stayed dry".format(TRIES, n_dry/TRIES))