Solution: The total number of possible calibration configurations is $3^6$. To count favorable cases, choose 4 sensors to be in "precision mode" in $\binom{6}{4}$ ways, and the remaining 2 sensors can be in either of the other 2 settings, giving $2^2$ possibilities. The probability is $\frac{\binom{6}{4} \cdot 2^2}{3^6} = \frac{15 \cdot 4}{729} = \frac{60}{729} = \frac{20}{243}$. Thus, the final answer is $\boxed{\dfrac{20}{243}}$.Question: A tech startup founder wants to align two project timel

["Solution: The Least Common Multiple of 10 and 15 Months", "Aligning two project timelines with different cycle lengths is a classic problem in mathematics and project management. For a tech startup founder aiming to synchronize two project cycles—10 months and 15 months—the goal is to find the smallest time interval after which both timelines coincide. This moment is determined by the Least Common Multiple (LCM) of the two cycle lengths.", "Understanding the Least Common Multiple (LCM)\nThe LCM of two numbers is the smallest positive integer that is evenly divisible by both. For project cycles, the LCM represents the earliest point in time when both schedules realign perfectly.", "Given cycle lengths:\n- Project A: 10 months\n- Project B: 15 months", "Step 1: Prime Factorization\nBreaking the numbers into prime factors helps compute the LCM efficiently:\n- $10 = 2 \ imes 5$\n- $15 = 3 \ imes 5$", "Step 2: Compute LCM\nThe LCM is found by taking the highest power of all primes appearing in the factorizations:\n- Prime 2: max exponent = 1 → $2^1$\n- Prime 3: max exponent = 1 → $3^1$\n- Prime 5: max exponent = 1 → $5^1$", "So,\n$$\n\ ext{LCM}(10, 15) = 2 \ imes 3 \ imes 5 = 30\n$$", "Conclusion\nThe least number of months after which both project timelines synchronize is 30 months. After this point, the original scheduling patterns will realign.", "Thus, the final answer is $\boxed{30}$."]