MathDB
2021 Combo #10: Dependent chance of coin

Source:

May 30, 2021
Combo

Problem Statement

Jude repeatedly flips a coin. If he has already flipped nn heads, the coin lands heads with probability 1n+2\tfrac{1}{n+2} and tails with probability n+1n+2.\tfrac{n+1}{n+2}. If Jude continues flipping forever, let pp be the probability that he flips 33 heads in a row at some point. Compute ⌊180p⌋.\lfloor 180p \rfloor.
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