Introduction to Probability (Bertsekas, 2nd edition)

Python Programming

Looking at problem 6, write a Python program to roll a six sided die where the faces come up with the probabilities in the problem. Run it for n = 10, 100, 1000, 10000, 100000. Do the percentages agree with your solution for problem 6? Please provide indented code as well. Thanks

Problem 6 Question - . A six-sided die is loaded in a way that each even face is twice as likely as each odd face. Construct a probabilistic model for a single roll of this die, and find the probability that a 1, 2, or 3 will come up.

Problem 6 Answer- Let c denote the probability of a single odd face. Then the probability of a single even face is 2c, and by adding the probabilities of the 3 odd faces and the 3 even faces, we get 9c = 1. Thus, c = 1/9. The desired probability is P({1, 2, 3}) = P({1}) + P({2}) + P({3}) = c + 2c + c = 4c = 4/9.