ISyE 3770 — Spring 2026 Homework #2 | Complete Solutions | 100% Updated.

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? 2. Using the same setup from problem 1, are A and B independent? Why or why not? Justify your response mathematically. 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? 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? 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? 8. Using the setup from problem 7, if you were to pick a dragon at random and see that it was not wealthy, what is the probability that this dragon is Ancient? 9. Using the setup from problem 7, Are the age of a dragon and their wealth independent? Why or Why not? 10. Suppose you’re in charge of watching a small child who really enjoys ice cream, but only eats chocolate, vanilla, or rocky road ice cream, and only ever one flavor at a time. Let E be the event that the child eats too much ice cream, and let C, V , and R represent the child eating chocolate, vanilla, and rocky road respectively. After many, many ice cream sessions, you’ve determined that the child eats chocolate ice cream 40% of the time, vanilla ice cream 25% of the time, and rocky road ice cream 35% of the time. You also know that the child overeats 20% of the time when served chocolate ice cream, 5% of the time when served vanilla ice cream, and 15% of the time when served rocky road ice cream. What is the overall probabilty that the child will overeat when served ice cream (regardless of flavor)? If you know that the child has eaten too much ice cream, what is the probability that they were served vanilla ice cream? If you know that the child has eaten ice cream, but didn’t eat too much, what is the probability that they were served chocolate or rocky road ice cream? 11. Suppose you have 3 red marbles, 2 green marbles and 1 blue marble and are lining them up in a row. If you do this completely randomly, compute the following probabilities: (a) What is the probability that the two outermost marbles are red? (i.e. position 1 and position 6) (b) What is the probability that one of the outermost marbles is green? (c) What is the probability that neither of the outermost marble is red?