Question

2. In my youth, I had friends who played AD&D. If my character is attacked, there is a 25% chance the attack will be successful (and damage from that attack is determined by rolling a fair 10-sided die with the resulting value subtracted from the character's current hit points) You should be familiar with dice, but just in case: the values on the dice are numbered sequen- tially starting at 1 a. With a fair 8-sided die, what values would I have to throw (or "roll") for an attack to fail? b. The attack was successful, what is the probability that my character will receive exactly 3 hit points of damage? c. The attack was successful, what is the probability that my character will receive 4 or fewer hit points of damage? d. My character only had 9 hit points of life remaining when the attack was successful. What is the probability he will die? fa character dies when the hit points go to 0 or below

Answer 1

b). Let S 0 or 1 if the attack was a fail or success. Thus S follows Bernoulli with p=0.25.

We need to find here P(X=3|s=1), where X denotes the damage or the roll of the 10-sided fair die. as the die is fair P(X=i)=0.1 for all i={1,2,3,...10}. Thus P(X=3|S=1)= 0.1.

c)Here we need to find P(X<=4)=4*0.1 = 0.4

d) The character will die if X=9 or 10 thus P(character will die)= P(X=9,10) = 0.2