Consider a product whose path through a supply chain is given in the previous figure. Suppose that each inspection point could select the product for inspection with the same probability equal to 0.50. Then answer the following questions: 

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

• And the probability of not being inspected at any checkpoint?

Each checkpoint 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 could be considered as a sum of two random variables that will result in a Binomial distribution.

To answer the previous question, the Binomial distribution can be used with the following parameters: n = 2, p = 1 − p = q = 0.5, and x = 1. 

• Happen exactly one inspection (one in each checkpoint): p(x = 1) = 2(0.5)(0.5) = 0.5 

• None inspection in all checkpoints: p(x = 0) = 0.25.

from scipy.stats import binom

import matplotlib.pyplot as plt

import numpy as np

# computing P(X) for each X.

x = [0, 1, 2]

n = 2

p = 0.5

y = binom.pmf(x, n, p)

print('  X  |',x)

print('P(X) |',y)

   X | [0, 1, 2] 

P(X) | [0.25 0.5 0.25]