Umbrellas Riddler

umbrellas.py

#!/usr/bin/env python

from itertools import product

PROB_MORNING_RAIN = .5
PROB_EVENING_RAIN = .4


# Enumerate all possible cases, and sum the probability of getting rained on
total_probability = 0  # Total probability of getting rained on

for rains in product(*[[True, False]]*10):
    # Calculate the probability of outcome and whether Louie was rained on
    rained_on = False
    probability = 1.0
    home, office = 2, 1  # Number of umbrellas at each location
    for i in range(5):
        # Morning
        if rains[2 * i]:
            probability *= PROB_MORNING_RAIN
            if home > 0:
                home -= 1
                office += 1
            else:
                rained_on = True
        else:
            probability *= 1 - PROB_MORNING_RAIN
        # Evening
        if rains[2 * i + 1]:
            probability *= PROB_EVENING_RAIN
            if office > 0:
                office -= 1
                home += 1
            else:
                rained_on = True
        else:
            probability *= 1 - PROB_EVENING_RAIN
    # Add resulting probability if Louis got rained on
    total_probability += probability if rained_on else 0

print(total_probability)  # 0.3073