Question

We're playing Chinese Whispers. I choose a digit, 0 or 1, and whisper it to a person sitting next to me. With probability p∈(0,1), the person hears it correctly and with probability 1−p hears the wrong digit. That person whispers the the next person, etc. repeating the pattern each time independently. What is the probability that the n-th person will hear the correct digit? Find the limit when n→∞. Why you're not surprised?

Answer 1

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