Biased coin

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, \(p=\mathbb{P}(Heads).\)

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

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