Each night the casino runs a '50-50' draw. Anybody can buy a ticket for $5, and at the end of the night a single ticket is drawn to determine the winner. The winner gets 50% of the money, the remaining money goes to the casino. Julie has bought the first ticket to the draw. The number of additional tickets sold follows a Poisson process with a rate of 4 per hour. The draw is made 2 hours after tickets begin to be sold. (a) What is the probability there are 6 additional tickets sold in a hour (not including Julie's ticket)? (b) What is the expected value of the prize? (c) What is the probability that Julie wins the draw?