Suppose we roll a fair six-sided die and then pick a number of cards from a well-shuffled deck equal to the number showing on the die. (For example, if the die shows 4, then we pick 4 cards.)
(a) What is the probability that the number of jacks in our hand equals 2?
(b) Conditional on knowing that the number of jacks in our hand equals 2, what is the conditional probability that the die showed the number 3?