Ten thousand raffle tickets are sold for $5 each. Four prizes will be awarded: one for $5000, one for $2500, and two for $1000. Assume that the probability that any given ticket is selected for the $5000 prize is 1/10,000, the probability that any given ticket is selected for the $2500 prize is 1/10,000 , and the probability that any given ticket is selected for a $1000 prize is 2/10,000. Sidhardt purchases one of these tickets.

(a) Determine his expected value.

(b) Determine the fair price of a ticket.