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is it good to drink distilled water - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Thus, the number of lattice points is:

📌 To determine the probability that exactly two out of three rolls of a fair six-sided die result in a 4, we can approach this using the binomial probability formula, since each roll is independent and has two outcomes of interest: rolling a 4 or not.

📌 We want the probability of exactly 2 successes in 3 trials:

📌 But because the arrangement is circular, we must be careful with wrap-around cases (i.e., positions 5,6,1,2 or 6,1,2,3 possible).

📌 Because this is complex for a math olympiad and must have a clean answer, we consider symmetry and known results or constructive counting.

📌 But given time and olympiad style, and since the circle wraps, we proceed with case analysis on placements of AAAA.

📌 Possible placements of 4 consecutive As in a circle of 6:

📌 But overlaps make inclusion-exclusion messy.

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