You decide to play a game where you flip a coin and record heads as a measure of success. a) Assume you flip the coin 30 times and observed a score of 18 heads. If you treat this as drawing from a Bernoulli distribution then what was the chance you observed an outcome at least as extreme as you have?b) Assume you flip the coin 900 times and for every 30 flips you happened to always observe a score of 18 heads consistently. If you treat this as drawing from a Binomial distribution then what was the chance you observed an outcome at least as extreme as you have?

c) Approximately what would your sample average need to be in part b) to make it equally extreme as the sample average in part a) was?