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:
$$\Pr(\mbox{fair}|A)=\frac{\Pr(A|\mbox{fair})\Pr(\mbox{fair})}{\Pr(A|\mbox{fair})\Pr(\mbox{fair})+\Pr(A|\mbox{biased})\Pr(\mbox{biased})}$$
This exercise is part of the course
Foundations of Probability in R
Exercise instructions
- 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.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Use dbinom to find the probability of 16/20 from a fair or biased coin
probability_16_fair <-
probability_16_biased <-
# Use Bayes' theorem to find the posterior probability that the coin is fair