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> 1−(1−1/32)^1 ≈ 3.1%.

This is a nice technique, but I find this math is somehow missing some scale-awareness. Suppose we had taken our "period" for assessing the per-period probability to be months instead of years. Then we would have calculated a 1/(30*12 + 2) = 0.002762430939 per-month chance of satellite attack, and substituting in values appropriately to the above equation, we would get a slightly higher chance

1 - (1 - 1/(30*12 + 2))^12 ≈ 3.26%

If we had taken it to be a decade, then we would have calculated a 1/(3 + 2) = 0.2 per-decade chance of satellite attack, and substituting in values, we would get something lower:

1 - (1 - 1/(3 + 2))^(1/10) ≈ 2.21%

Is there some art to choosing the period over which we average? Is it a good idea to take the limit as the period gets smaller and smaller?

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