A magician has two coins: one is unbalanced and lands heads 60% of the time; the other is fair and lands heads 50% of the time. A member of the audience randomly selects one of the coins and flips it. The result is heads.
a. What is the prior probability that the fair coin was selected?
b. Given additional information in the form of the single flip that came up heads, what is the revised probability that the coin is the fair one?