No two neighboring bulbs lit
Each of the bulbs in a grid is independently on with probability . What is the probability that no two edge-adjacent bulbs (cells sharing a side) are both on?
Show hints (2)+
- All patterns are equally likely; count the valid ones (independent sets of the grid).
- A row-by-row transfer count gives independent sets, so .
Answer
Reveal answer →Final answer
0.123 (± 0.002)
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Asked at: Jane Street, Two Sigma