66. Consider an urn containing a large number of coins and suppose that each of the coins has some probability p of turning up heads when it is flipped.

However, this value of p varies from coin to coin. Suppose that the composition of the urn is such that if a coin is selected at random from the urn, then its p-value can be regarded as being the value of a random variable that is uniformly distributed over [0, 1]. If a coin is selected at random from the urn and flipped twice, compute the probability that

(a) the first flip is a head;

(b) both flips are heads.