A famed baker decides to go for one last run of contests. The contest is held annually.
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Question:
A famed baker decides to go for one last run of contests. The contest is held annually. There is a 0.1 chance he takes first place, a 0.2 chance he takes second place, and a 0.3 chance he takes third place. He has decided to keep entering the contest every year until he places below third. Once he places below third, he will give up and stop competing. First place had a prize of $1000, second place has a prize of $500, and third place had a prize of $100. What is the expected value of the baker's profit at the end of his contest streak?
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