Question

Guo is playing Advanced Dungeons & Dragons (AD&D), 2nd edition. His character, Xenu the Destroyer, is...

Guo is playing Advanced Dungeons & Dragons (AD&D), 2nd edition. His character, Xenu the Destroyer, is

wielding a specially made sword, the golden-hilted sword, that can inflict damage from 3-12 hit points. Guo has just

hit a Hill Giant, Uther the Strong. If he can inflict 10 or more points of damage on Uther, then Xenu vanquishes Uther.

There are two ways to generate a range of numbers between 3-12 using the common dice available. One way is to role

a single ten-sided die and add two (1d10+2) and the other way is to role three four-sided die (3d4). (a) If Guo roles

the 1d10+2, what is the probability of killing Uther? (b) If he instead roles 3d4, what are his chances of killing Uther?

Ans: In order to kill uther he has to do damage of 10 or more that is 10,11 or 12.

a) If he rolls 1d10+2 he needs to get 8 or more in order to get total of 10 or more.

P(getting 8 or more in a single throw of a die with 10 sides) =

Therefore the probability of killing uther =

b) if he rolls 3d4 total possible outcomes = 4x4x4 = 64

favourable outcomes = (4,4,2)x 3 ways + (4,3,3)x 3 ways + (4,4,3)x 3 ways + (4,4,4)x 1 way = 10

P(getting total 10 or more) =

Therefore the probability of killing uther =