Suppose we flip two fair coins and roll one fair six-sided die.
(a) What is the probability that the number of heads equals the number showing on the die?
(b) What is the conditional probability that the number of heads equals the number showing on the die, conditional on knowing that the die showed 1?
(c) Is the answer for part (b) larger or smaller than the answer for part (a)? Explain intuitively why this is so.