You will use probability distributions to optimize the selection of combat tools against various fictional opponents Suppose you are trained in the use of five weapons dagger, spear, axe, sword, and polearm The damage caused by each of these sharp instruments of death is summarized in the table below Dagger Spear Axe Sword Polearm d4 4 d6 3 d8 2 d10 1 d12 (Recall that the notation d4 means the result of rolling a 4 sided die, etc ) Construct a probability distribution for X , the amount of damage dealt by one blow of a weapon, for each weapon (five distributions) Using your distributions, confirm that the expected damage output for each weapon is the same Upon hearing this, your friend scoffs, If the expected damage is the same for every weapon, it doesn't matter which you choose Explain briefly why he is wrong Your explanation should include what differs among these distributions After your explanation, your friend is still giving you a blank stare You decide to illustrate your point with some examples After computing each of the below, summarize the results with a written description using complete sentences Demonstrate, using probabilities, why a dagger is a clearly preferable choice when fighting kobolds with five hit points each (a kobold is defeated after receiving five damage) Specifically, this means to compute the probability you defeat the kobold by hitting it with each of the weapons Compare the probabilities of defeating a seven hit point goblin with one stroke of each weapon (it should be the same for each weapon) Show that either a dagger or spear is equally preferable by computing the probability that two strokes of each weapon will be sufficient It is impossible to defeat an orc, with nine hit points, with one stroke of a dagger Which weapon is most likely to fell an orc with a single blow (compute each probability) Which weapon is most likely to fell an orc in at most two blows (compute each probability) Only with a polearm can you defeat a hobgoblin, with twelve hit points, with a single strike Compute the probability of defeating it using no more than two blows of each weapon, and then the probability of needing at most three strokes

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You will use probability distributions to optimize the selection of combat tools against various fictional opponents. Suppose you are trained in the use of five

You will use probability distributions to optimize the selection of combat tools against various fictional opponents.

Suppose you are trained in the use of five weapons: dagger, spear, axe, sword, and polearm. The damage caused by each of these sharp instruments of death is summarized in the table below:

Dagger	Spear	Axe	Sword	Polearm
d4+4	d6+3	d8+2	d10+1	d12

(Recall that the notation "d4" means the result of rolling a 4-sided die, etc.)

Construct a probability distribution for X, the amount of damage dealt by one blow of a weapon, for each weapon (five distributions).
Using your distributions, confirm that the "expected damage output" for each weapon is the same.
Upon hearing this, your friend scoffs, "If the expected damage is the same for every weapon, it doesn't matter which you choose." Explain briefly why he is wrong. Your explanation should include what differs among these distributions.
After your explanation, your friend is still giving you a blank stare. You decide to illustrate your point with some examples. After computing each of the below, summarize the results with a written description using complete sentences.
Demonstrate, using probabilities, why a dagger is a clearly preferable choice when fighting kobolds with five hit points each (a kobold is defeated after receiving five damage). Specifically, this means to compute the probability you defeat the kobold by hitting it with each of the weapons.
Compare the probabilities of defeating a seven hit point goblin with one stroke of each weapon (it should be the same for each weapon). Show that either a dagger or spear is equally preferable by computing the probability that two strokes of each weapon will be sufficient.
It is impossible to defeat an orc, with nine hit points, with one stroke of a dagger. Which weapon is most likely to fell an orc with a single blow (compute each probability)? Which weapon is most likely to fell an orc in at most two blows (compute each probability)?
Only with a polearm can you defeat a hobgoblin, with twelve hit points, with a single strike. Compute the probability of defeating it using no more than two blows of each weapon, and then the probability of needing at most three strokes.