Probability Distributions

In this lesson, we’ll discuss different ways probability can be distributed across the different outcomes of the experiment and explore some examples of probability distributions. To begin understanding probability distributions, you’ll look at a visualization depicting the probability of each dice roll of a fair six-sided dice.

Knowing how probability is distributed is important because it tells us many important things about the experiment, such as:

  • What outcomes has the highest probability associated with it?
  • What would be the probability of observing a range of outcomes instead of just a single one?

In Probability Fundamentals in R, we learned about some of the basic ideas behind probability: what it represents, how to calculate it and some rules for approaching our calculations. We motivated our examples using coins, dice and cards since they represent real-world examples of the concepts we covered. In all the examples used in the course so far, we had the same implicit assumption: the probability of observing any single outcome is equally likely. Throughout this lession, you will find out that assumption is now always the case.

As you learn about probability distributions, you’ll get to apply what you’ve learned from within your browser so that there’s no need to use your own machine to do the exercises. The Python environment inside of this course includes answer checking so you can ensure that you’ve fully mastered each concept before learning the next concept.


  • Learn the basics of probability distribution
  • Understand the probability of combinations of events using the binomial distribution
  • How the normal distribution works

Lesson Outline

  1. Distribution of Probability
  2. Useful Qualities of Probability Distributions
  3. The Probability Distribution Function
  4. Example: Sum of Two Dice Rolls
  5. Cumulative Probability
  6. From Random Experiments to Actual Experiments
  7. The Normal Distribution
  8. Probability Distribution Function for the Niormal
  9. Cumulative Probability for the Normal
  10. Next Steps
  11. Takeaways

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