this post was submitted on 24 Nov 2024
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For the probability that at least one arrow picked is cursed: 1/2 + 1/2 × 5/9 = 14/18 = 7/9. (The probability that you picked it the first time, plus the probability that you missed it the first time but picked it the second time).
a dice probability calculator tells me probability of 3d6 + 1d4 at least 16 is 2/9. So the DM is correct.
The math is easier if you look for the probability that the arrows are safe. If you do it that way, it's simply 1/2*4/9, or 2/9.
That is true. Cueball had asked the question in the way I described, but the check was done in the inverse which is easier to do the math on.