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ZOOM 8) 9) 2 A gambler is told that one of three slot machines pays off with probability 1/2, while each of the other two pays off with probability 1/3. Draw a tree diagram to help you. (4 pts) a) If the gambler selects one machine at random and plays it twice, what is the probability that he will lose the first time and win the second? (4 pts) b) If the gambler loses the first time and wins the second, what is the probability he chose the favorable machine? (4 pts) You purchase a raffle ticket to help out a charity. The raffle ticket costs $5. The charity is selling 2000 tickets. One of them will be drawn and the person holding the ticket will be given a prize worth $4000. Compute the expected value. (6 pts)