I have two ordinary decks of cards (4 suits, 13 denominations, the usual); the two decks have different back designs, so I can easily tell which is which. I shuffle all the cards together and, without looking, take two cards uniformly at random and put them in my pocket. Let E be the event that my two cards came from the same deck, and let F be the event that my two cards are the same suit (whether they came from the same deck or not).
a) Compute P(E|F).
b) Compute P(F |E).
c) Are the events E, F independent? Why or why not?