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  3. Foundations of Probability in R

Exercise

More updating with priors

Suppose we see 16 heads out of 20 flips, which would normally be strong evidence that the coin is biased. However, suppose we had set a prior probability of a 99% chance that the coin is fair (50% chance of heads), and only a 1% chance that the coin is biased (75% chance of heads).

You'll solve this exercise by finding the exact answer with dbinom() and Bayes' theorem. Recall that Bayes' theorem looks like:

$$\Pr(\mbox{fair}|A)=\frac{\Pr(A|\mbox{fair})\Pr(\mbox{fair})}{\Pr(A|\mbox{fair})\Pr(\mbox{fair})+\Pr(A|\mbox{biased})\Pr(\mbox{biased})}$$

Instructions

100 XP
  • Use dbinom() to calculate the probabilities that a fair coin and a biased coin would result in 16 heads out of 20 flips.
  • Use Bayes' theorem to find the posterior probability that the coin is fair, given that there is a 99% prior probability that the coin is fair.