HMMT 2006 U39
- Guts
- Answer
A fat coin is one which, when tossed, has a probability of being heads, of being tails, and of landing on its edge. Mr. Fat starts at 0 on the real line. Every minute, he tosses a fat coin. If it's heads, he moves left, decreasing his coordinate by 1 ; if it's tails, he moves right, increasing his coordinate by 1 . If the coin lands on its edge, he moves back to 0 . If Mr. Fat does this ad infinitum, what fraction of his time will he spend at 0 ?
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{1}{3}
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