Poisson Probability

Code : 

import math

# Questions are translated from https://www.youtube.com/watch?v=3-539wQLCaQ

#Example 1
#A tire company producing tires during 5 days in a week. 4 of tires averagely 
#are failed in a weekly based production. What is the probability
#of at least 3 failed tires production in a day in the company, 

def poisson_probability(actual, mean):
    # naive:   math.exp(-mean) * mean**actual / factorial(actual)
    
    # iterative, to keep the components from getting too large or small:
    p = math.exp(-mean)
    for i in xrange(actual):
        p *= mean
        p /= i+1
    return p

def example1():
    mean = 4./5
    prob = poisson_probability(0,mean) + poisson_probability(1,mean) + poisson_probability(2,mean) 
    prob = 1 - prob
    percent_str = '{:.2%}'.format(prob)
    print("EX1 : At least 4 damaged tyres pw so the probability of 3 damaged pw : %", percent_str)

def example2():
    mean = 3*2    #mean for 2 decares
    prob = poisson_probability(5,mean) 
    percent_str = '{:.2%}'.format(prob)
    print("EX2(a) : The probability of drying out for 5 of them : %", percent_str)
    
    prob = poisson_probability(0,mean) + poisson_probability(1,mean) + poisson_probability(2,mean) 
    percent_str = '{:.2%}'.format(prob)
    print("EX2(b) :The probability of drying out for max 2 of them : %", percent_str)
    
    
if __name__ == '__main__':
    example1()
    example2()
    pass

Output : 

(‘At least 4 damaged tyres pw so the probability of 3 damaged pw : %’, ‘4.74%’)
(‘The probability of drying out for 5 of them : %’, ‘16.06%’)
(‘The probability of drying out for max 2 of them : %’, ‘6.20%’)

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