Phuc is playing Dungeons and Dragons with a group of three f

Phuc is playing Dungeons and Dragons with a group of three friends. To heal an injured friend\'s character. Phuc must roll one die and roll a number higher than that friend\'s damage level. This turn, Phuc can roll one die for each of his friends (i.e. 3 dice in total). Phuc\'s friends have damage levels: 16. 5 and 14 respectively. If Phuc uses a 20-sided die, what is the probability that Phuc heals all his friends this turn after completing his three rolls?

Solution

Probability of healing 1st friend (P1) = 4/20 = 0.2

Probability of healing 2nd friend (P2) = 15/20 = 0.6

Probability of healing 3rd friend (P3) = 6/20 = 0.3

Probability that he heals all his friends = P1 * P2 * P3 = 0.2*0.6*0.3 = 36/1000=0.036