Exercise

Updating with Bayes theorem

In this chapter, you used simulation to estimate the posterior probability that a coin that resulted in 11 heads out of 20 is fair. Now you'll calculate it again, this time using the exact probabilities from dbinom(). There is a 50% chance the coin is fair and a 50% chance the coin is biased.

Instructions

100 XP

Use the dbinom() function to calculate the exact probability of getting 11 heads out of 20 flips with a fair coin (50% chance of heads) and with a biased coin (75% chance of heads). Save them as probability_fair and probability_biased, respectively.
Use these to calculate the posterior probability that the coin is fair. This is the probability that you would get 11 from a fair coin, divided by the sum of the two probabilities.