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.