A standard deck of playing cards has 52 cards in four suits (two red, two black), each suit with cards numbered 2{10 and \face cards" labelled jack, queen, king, and ace. A \pinochle deck" has 48 cards: each of the four suits has only 9 and 10 plus the face cards, and each card appears twice in the deck.

Assuming in each case that the relevant deck is well-shued, identify the fol- lowing probabilities. Show your work by making it clear where each number in your probability comes from.

a. p(R=ace j D=standard): In a standard deck, the probability of draw- ing any card whose rank is `ace'

b. p(R=ace j D=pinochle): In a pinochle deck, the probability of drawing any card whose rank is `ace'

c. p(F=true, C=red j D=pinochle): the probability of drawing a card whose rank is one of the face cards and whose suit is one of the red suits, from a pinochle deck

d. p(R=A, S=H j F=true): the probability of drawing the ace of hearts given that the card drawn is a face card

e. If there are 3 standard decks and 1 pinochle deck in a pile, and you pick one at random before drawing a card from that deck, what is p(F=true), i.e. the overall probability of drawing a face card?