You have a fair coin and a biased coin, but you can’t tell which is which. The biased coin lands on heads 75% of the time. You decide to try to determine which coin is the biased coin by selecting one of the coins at random and flipping tn 100 times. Let \(\hat{p}\) be your observed fraction of heads. Based on \(\hat{p}\), you decide which coin is the biased one.

- For which values of \(\hat{p}\) will you assume the coin you flipped is the biased coin?
- What is the probability that you correctly determine which coin is the biased coin?