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ISyE 3770 — Spring 2026
Homework #2 – Due Thursday, Feb. 5th
Only the 1st five problems will be graded, any additional problems are for practice.
1. Suppose you are an anthropoligist/biologist in a fantasy world, and you’re studying
minotaurs. Let A be the event that a minotaur is at least 7 ft tall and B be the
event that it weighs at least 325 lbs.
After extensive studies, you’ve found that P (A) = 0.525, P (B) = 0.475, and
P (A ∩ B) = 0.35.
Being an expert on minotaur biology, you decide that a minotaur should be
classified as very large (a very technical term) if they are at least 7 ft tall and if
they weigh at least 325 lbs, and a minotaur should be classified as large if it meets
only one of these two criteria. If you encounter a minotaur in the wild, what is the
probability that they would be classified as large?
P(large)=P(A only)+P(B
only)=(P(A)−P(A∩B))+(P(B)−P(A∩B))=(0.525−0.35)+(0.475−0.35)=0.175+0.125=0.3
2. Using the same setup from problem 1, are A and B independent? Why or why
not? Justify your response mathematically.
Events AA and BB are independent if P(A∩B)=P(A)P(B)P(A∩B)=P(A)P(B).
P(A)P(B)=0.525×0.475=0.249375≠0.35P(A)P(B)=0.525×0.475=0.249375 =0.35.
Hence they are not independent.
3. Using the same setup from problem 1, Suppose you bump into a minotaur that
is at least 7 feet tall in the wild. Given that this minotaur is at least 7 feet tall,
what is the probability that it weighs at least 325 lbs?
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4. Suppose you are playing a board game. To determine how many spaces you get to
move, you flip a coin. If the result is tails, you roll a single six-sided die and move
that many spaces. If the result is heads, you roll a single 12-sided die and move
that many spaces.
What is the probability that you move at least 5 spaces in a single turn?
5. Continuing from problem 4, what is the probability that you move between 2 and
7 spaces (including 2 and 7) in a single turn?
6. Continuing from problem 4, is the result of the coin toss independent of the value
of the die rolled? Why or Why not?
No, the coin toss and die value are not independent because the probability of a
particular die outcome depends on which side of the coin appears. For
instance, P(die=1∣heads)=1/12P(die=1∣heads)=1/12 while P(die=1)=1/8P(die=1)=
1/8, and these are not equal.
7. Now suppose you’re a fantasy economist. After years of study and a fantasy
census, you’ve determined that 20% of all dragons can be classified as Ancient
(they’re really old). Of these ancient dragons, 85% of them can be considered
wealthy (even by dragon standards). For all other dragons, only 10% of them
could be considered wealthy.
Using this, if you were to pick a dragon at random, what is the probability that
they would be considered wealthy?
ISyE 3770 — Spring 2026
Homework #2 – Due Thursday, Feb. 5th
Only the 1st five problems will be graded, any additional problems are for practice.
1. Suppose you are an anthropoligist/biologist in a fantasy world, and you’re studying
minotaurs. Let A be the event that a minotaur is at least 7 ft tall and B be the
event that it weighs at least 325 lbs.
After extensive studies, you’ve found that P (A) = 0.525, P (B) = 0.475, and
P (A ∩ B) = 0.35.
Being an expert on minotaur biology, you decide that a minotaur should be
classified as very large (a very technical term) if they are at least 7 ft tall and if
they weigh at least 325 lbs, and a minotaur should be classified as large if it meets
only one of these two criteria. If you encounter a minotaur in the wild, what is the
probability that they would be classified as large?
P(large)=P(A only)+P(B
only)=(P(A)−P(A∩B))+(P(B)−P(A∩B))=(0.525−0.35)+(0.475−0.35)=0.175+0.125=0.3
2. Using the same setup from problem 1, are A and B independent? Why or why
not? Justify your response mathematically.
Events AA and BB are independent if P(A∩B)=P(A)P(B)P(A∩B)=P(A)P(B).
P(A)P(B)=0.525×0.475=0.249375≠0.35P(A)P(B)=0.525×0.475=0.249375 =0.35.
Hence they are not independent.
3. Using the same setup from problem 1, Suppose you bump into a minotaur that
is at least 7 feet tall in the wild. Given that this minotaur is at least 7 feet tall,
what is the probability that it weighs at least 325 lbs?
, 2
4. Suppose you are playing a board game. To determine how many spaces you get to
move, you flip a coin. If the result is tails, you roll a single six-sided die and move
that many spaces. If the result is heads, you roll a single 12-sided die and move
that many spaces.
What is the probability that you move at least 5 spaces in a single turn?
5. Continuing from problem 4, what is the probability that you move between 2 and
7 spaces (including 2 and 7) in a single turn?
6. Continuing from problem 4, is the result of the coin toss independent of the value
of the die rolled? Why or Why not?
No, the coin toss and die value are not independent because the probability of a
particular die outcome depends on which side of the coin appears. For
instance, P(die=1∣heads)=1/12P(die=1∣heads)=1/12 while P(die=1)=1/8P(die=1)=
1/8, and these are not equal.
7. Now suppose you’re a fantasy economist. After years of study and a fantasy
census, you’ve determined that 20% of all dragons can be classified as Ancient
(they’re really old). Of these ancient dragons, 85% of them can be considered
wealthy (even by dragon standards). For all other dragons, only 10% of them
could be considered wealthy.
Using this, if you were to pick a dragon at random, what is the probability that
they would be considered wealthy?
