RNG Combat
You are a level 1 with a starter sword, however, the sword's durability is very low. The sword can only do 4 hits, does 1 to 3 damage distributed uniformly and ignoring critical hits.
Your quest is to kill a mob that has 10 HP.
What is the probability that you kill the mob in 4 hits?
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1 solution
We can get a score greater than 10 in each of the following ways. We can get "all threes" (there is one way to do this), by getting a score of the form (3, 3, 3, 1) (there are four ways to do this - the "one" can be in any of the four places), by getting a score of the form (3,3,3,2) (there are four ways to do this), or by getting a score of the form (3,3,2,2) (there are 6 ways this can happen). Summing shows that the total possible ways to get at least 10 are:
1+4+4+6 = 15.
In total, there are 3^4 = 81 total outcomes.
Therefore:
Probability of score of at least 10 = 15/81 = 5/27