Ex1 A warrior strikes an orc in a role playing game. The warrior misses (M) if a 20-sided die rolls 15 or less. An ordinary hit (H) occurs if it rolls 16-19. A critical hit (C) occurs on a 20. A miss fails to deal any damage to the orc. Hits do damage (V). An ordinary hit does damage equal to the sum of the rolls of two 4-sided dice. A critical hit does four 4-sided dice worth of damage. (The dice in this exercise are independent from each other and fair with sides having numbers 1, 2, ...,n where n is the number of faces of that die.) (a) Deduce the probability distribution of damage V done by an ordinary hit H and write it out in the form of 2 3 ... (2p) P( V = v |H) ? ? ... (b) Calculate, according to the previous part or otherwise, what is the probability of dealing at least 6 damage on an ordinary hit P(V 2 6 | H). (1p) (c) What is the probability of dealing at least 6 damage on a critical hit P(V 2 6 | C)?(2p) (d) Without assuming hits or misses, what is the probability that an orc that can take 6 points of damage will be felled by the first attempted strike? (1p)