You have a biased coin, but you don’t know what the bias is. Let \(p\) be the actual probability of getting heads on a single coin flip, \(p=\mathbb{P}(Heads).\)

- Suppose \(p=0.8\). What is the probability of observing between 76 and 84 heads out of 100 flips of the coin.
- Suppose you flip the coin 100 times and observe 80 heads. What is the 95% confidence interval for \(p\)?