By Department of Mathematics
Deadline: 11:59 PM on Sunday, Sept. 22
The contest is open to everyone. Individuals or teams of at most three members may submit solutions. Do not discuss the problem with anyone other than members of your team. You may use any source, written or electronic, but all sources must be properly cited. You may use any computational tools. Your solution will be graded on a 0–4 point scale. All your assertions must be completely and fully justiﬁed. At the same time, you should aim to be as concise as possible; avoid overly lengthy arguments and unnecessary components. Your grade will be based on both mathematical accuracy and clarity of presentation. Either send your solution to firstname.lastname@example.org or put it in Bela’s departmental mailbox by the above deadline. Consistently successful participants will receive the Paul Mugabi Mathematics Problem Solving Award.
Given a bowl containing orange and blue tokens, every day you remove one of the following: an orange token, a blue token, or both an orange token and a blue token – you make your decision randomly with probability 1/3 for each possibility. You stop as soon as you run out of either color. If the bowl originally contained 4 orange tokens and 4 blue tokens, what is the probability that the bowl is empty when you stop?