I ve solved the same problem without Bernoulli fourmula (binomial), just thinking, with 2 and 3 dice but could some of you help me to find out what is the probability of:
A) obtain with N dice attacking atleast one greather number than one Defence die? Not the sum of the N dice, but the greatest value of those N against another 1 die
B) All of them N are contemporary greater than the defense die?
If you want we can call the last one die D (Defense) and we can say that the others N dice are attacking
Without Bernoulli i ve found out with 2 dice A) $$1-\sum_{1}^{6} (\frac{k}{6})^{2} \cdot \frac{1}{6} $$
And B) $$\sum_{1}^{6} (1-\frac{k}{6})^{2} \cdot \frac{1}{6}$$ Please I need it so bad with Bernoulli or with the probability of Maximum