Consider a product whose path through a maritime route is given on the map. Now, suppose that each country port could be a potential risk point, and the probability of the cargo container suffering some adulteration is equal to the risk of the country. More factors could be considered. like depending on the cargo classification according to HS6 code, or port risk, but let's keep it simple. Then answer the following questions: 

• What is the probability of the product being selected affected one time for adulteration in this path? 

• And the probability of not being affected in any country port?

Each country could be considered a Bernoulli experiment since it could be successful (product not selected) or not (product selected). Supposing the checkpoints are independent, then the successive Bernoulli experiments with different probabilities pi are very small, you can use Poisson approximation. Let Xi∼Be(pi) be independent and let Y∼Po(λ) with λ=∑pi.  A classic paper by Hodges and Le Cam it is shown that.

To answer the previous question, and use the Poisson distribution can be used as an approximation using λ=∑pi, the below interactive map had been employed to obtain the following risk of each country:

• China - 0.24, Malaysia - 0.66, Sri Lanka - 0.37, Yemen - 0.46, Egypt - 0.56, Spain - 0.26, and France - 0.52. The total sum of probabilities is λ=∑pi = 3.07.

from scipy.stats import poisson

import matplotlib.pyplot as plt

import numpy as np

mu = 3.07

x = np.arange(0, 20, 1)

y = poisson.pmf(x, mu)

plt.plot(x,y,'r-',x, y,'bo')

plt.show()