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Originally Posted by manger
I think the stat table is incorrect for arocloth. Check my reasoning please, but the probability of saving an elf life is # of ways the event can occur divided by the total number of outcomes (I.E. probablility).
the number of ways the event can occur is: 7
10 ullar symbols - 3, the 3 being no ullar symbols, 1 ullar symbol and 2 ullar symbols, none of which could save a life.
the total number of outcomes is 6 different chances per dice x 10 dice, therefore you have a 7/60 chance to save an elf each time an elf is destroyed... 11.6% chance. even worse than what you predicted in your table.
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Wow! Your math is way off!
There are 10C3 = 10!/((10-3)!3!) = 120 ways that just 3 ullar symbols can be rolled on 10 dice.
The probability, p, of the event that one ullar symbol is rolled on a die is:
# of occurrences/total # of outcomes = 1/6
The probability, q, of the event that any other symbol is rolled on a die is:
1- p = 1- 1/6 = 5/6
The probability that
exactly 3 ullar symbols are rolled on 10 dice is:
120*(1/6)^3*(5/6)^7 = ~0.1550 = 15.50%
which comes from the binomial probability function:
p(n) = mCn*p^(n)*q^(m-n)
Now, if we want to know the probability of the event that
at least 3 ullar symbols are rolled on 10 dice that is:
p(n>=3) = sum(p(n),3,10) = 1- sum(p(n),0,2) = 0.2248 = 22.48%