1
The binomial distribution
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One of the simplest and most common examples of a random phenomenon is a coin flip: an event that is either "yes" or "no" with some probability. Here you'll learn about the binomial distribution, which describes the behavior of a combination of yes/no trials and how to predict and simulate its behavior.
2
Laws of probability
In this chapter you'll learn to combine multiple probabilities, such as the probability two events both happen or that at least one happens, and confirm each with random simulations. You'll also learn some of the properties of adding and multiplying random variables.
3
Bayesian statistics
Bayesian statistics is a mathematically rigorous method for updating your beliefs based on evidence. In this chapter, you'll learn to apply Bayes' theorem to draw conclusions about whether a coin is fair or biased, and back it up with simulations.
4
Related distributions
So far we've been talking about the binomial distribution, but this is one of many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial: the normal, the Poisson, and the geometric.

Initializing

Updating for other outcomes

In the last exercise, you solved for the probability that the coin is fair if it results in 11 heads out of 20 flips, assuming that beforehand there was an equal chance of it being a fair coin or a biased coin. Recall that the code looked something like:

probability_fair <- dbinom(11, 20, .5)
probability_biased <- dbinom(11, 20, .75)
probability_fair / (probability_fair + probability_biased)

Now you'll find, using the dbinom() approach, the posterior probability if there were two other outcomes.

Find the probability that a coin resulting in 14 heads out of 20 flips is fair.
Find the probability that a coin resulting in 18 heads out of 20 flips is fair.