Repainting balls to one color
A box has balls, each a different color. Repeatedly draw a random ordered pair of balls, repaint the first to match the second, and return both. Continue until all balls share one color. For , find the expected number of steps. (This system reduces to a symmetric random walk - you must identify its absorbing barriers to solve it.)
Show hints (2)+
- Track how many balls share one color - it is a symmetric random walk absorbing at and .
- Expected absorption time works out to ; then set .
Answer
Reveal answer →Final answer
16
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