Suppose that your friend has a loaded coin that comes up heads 80% of the time and another coin that looks just like the weighted one but is fair. Your friend pulls a coin at random out of his pocket and offers you a bet where he gets $1 if the heads side appears. You are a bit uncomfortable with this and insist on testing the coin. You flip it 5 times, and the heads side comes up once. Given this new information, how likely is it that you have the fair coin? Express your answer as a percentage.

Hint: You can use =BINOM.DIST() in Excel to compute the probabilities of the coin flips.

1) 74%

2) 88%

3) 98%

4) 96%