![]() If we assume that the outcome on has no impact on the outcome on (and vice versa), then the outcomes are independent. Our experiment is to roll both dice at the same time and observe which faces land up. ![]() Now assume that we have two fair six-sided dice, which are labelled so we can tell them apart. Each side can land face-up with probability. Independent Dice RollsĪ fair six-sided die has equally likely outcomes. I highly recommend these two sources to you, and hope that you find the approach I’ve taken here combines some of the best aspects of each.Ī Jupyter Notebook with the code and portions of the text from this post may be found here. Looking forward to future posts, we will analyze some interesting board games and start estimating win probabilities in basketball and baseball.Īs in the previous post, the Python framework developed here is inspired by and borrows from two excellent sources: Peter Norvig’s Concrete Introduction to Probability using Python and Allen Downey’s blog post on using the Python Counter class to represent probability mass functions. In this notebook, we’ll look at how even simple dice rolls result in unequal probabilities, and why we need distributions to represent the outcomes. That’s not a very realistic framework for analyzing sports or other real-world scenarios. Our previous discussion on classical probabilty only dealt with situations where all outcomes are equally likely. In this post, we will discuss the concept of probability distribution and how to represent it in Python. This post builds on the previous post on probability modeling in Python.
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