(20 points) Three cards from an ordinary deck of 52 cards are missing. A random card is drawn from this defective deck. Let E be the event that the randomly drawn card is a spade. Let F, be the event that i spades are missing from the 49-card defective deck, for i = 0, 1, 2, 3. a) Find P(Fo), P(F1), P(F2), P(F3). b) Find P(E|Fo), P(E F1), P(E| F2), P(E|F3). c) What is the probability that a random card drawn from this deck is a spade? Find P(E). Justify your answer, using the law of total probability. d) Find the probability that exactly 2 spades are missing from the deck, given that the drawn card was a spade. This is, find P(F2 | E)