Weather In Probability Land

Python Puzzles

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In Probability Land, on a sunny day there is an equal probability of the next day being sunny or rainy. On a rainy day, there is a 70% chance it will rain the next day, and a 30% chance it will be sunny the next day.

On average, how many rainy days are there in Probability Land?


It rains approximately 62% of the time in Probability Land.

import numpy as np
result = []

for _ in range(10_000):

    sunnydays = 0
    forecast = np.random.binomial(1,.7,1).item()
        
    for _ in range(365):
        if forecast == 1:
            sunnydays += 1
            forecast = np.random.binomial(1,.5,1).item()
        else:
            forecast = np.random.binomial(1,.3,1).item()
        
    result.append(sunnydays)

pct_rain = ((365 - (sum(result)/len(result)))/365)
print('It rains approximately ' + '{0:.0%}'.format(pct_rain) + ' of the time in ProbabilityLand.')