Suppose you’re playing air hockey with some friends and flip a coin to see who starts with the puck. After playing 12 times, you realize that the friend who brings the coin almost always seems to go first: 9 out of 12 times. Some of your other friends start to get suspicious. Define prior probability distributions for the following beliefs:

• One person who weakly believes that the friend is cheating and the true rate of coming up heads is closer to 70 percent.

• One person who very strongly trusts that the coin is fair and provided a 50 percent chance of coming up heads.

• One person who strongly believes the coin is biased to come up heads 70 percent of the time.