Two eight-sided dice both landing high

Question

You roll two fair eight-sided dice (faces 1 through 8). What is the probability that the smaller of the two values is at least 6?

Accepted Answer

The smaller value is at least 6 exactly when both dice land on 6, 7, or 8. Each die does so with probability \frac{3}{8}, and the two rolls are independent, so P(	ext{min} \ge 6) = \left(\frac{3}{8}ight)^2 = \frac{9}{64} \approx 0.141. Takeaway. The face count of the die only changes the fraction \frac{m-v+1}{m}; the "both clear the bar" logic is identical.

Two eight-sided dice both landing high

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