ISyE 3770 — Spring 2026 Homework #1 – Already Solved 100% Completed.

ISyE 3770 — Spring 2026 Homework #1 Only the 1st five problems will be graded, any additional problems are for practice. 1. Suppose I roll a four-sided die (like a standard die, but only has 4 sides), flip a coin, and record the paired results as the outcome of my experiment. What is the sample space of this experiment? 2. On any day that I have to proctor an exam, I go through the drive-through of a popular donut chain and get myself a little treat. I always buy myself exactly one beverage, either a hot chocolate or a sweet tea. I often also get myself something to eat as well: either a donut, an order of hashbrowns, a bagel, or possibly even some combination of the three. Since I am obviously obsessed with probability, I leave what I order up to complete chance (I’ll give you the full algorithm in a future assignment). Let’s define the events as follows: C is the event I order a hot chocolate, T is the event I order a sweet tea, D is the event I order a donut, H is the event I order hashbrowns, and B is the event I order a bagel. Given the above setup, if the probability I order a hot chocolate is 0.2, what is the probability I order a sweet tea? 3. Using the setup from problem 2, regardless of what I order to drink, the probability I order a donut is 0.35, the probability I order a bagel is 0.3, the probabilty I order hashbrowns is 0.45, the probability I order a donut and hashbrowns is 0.2, the probability I order a bagel and hashbrowns is 0.1, and I never order a bagel and donut together. Given this, what is the probability that I order a bagel and no hashbrowns? 2 4. The final event of the Grand Prix of Figure Skating consists of the top 6 individual skaters (or pairs of skaters for pairs or dance) based on how they performed in the Grand Prix. For the women’s event, how many different ways could we assign the gold, silver, and bronze medals? 5. Suppose that for the Grand Prix of Figure Skating Final, we are only concerned with who finishes on the podium, not what medal they received. How many different podiums could we have for the women’s event? 6. Carrying on with the setup from problem 2, what is the probability that the only food item I order is hashbrowns? 7. Yet again referencing problem 2, what is the probability that I order a bagel, a donut, or hashbrowns? What is the probabilty I order all three? 8. Play around with the donut example a bit more...sketch a few Venn diagrams, answer other probability questions, etc. 9. Answer the following questions using the setup from problem 1: (a) What is the probabilty that the die roll portion of my experiment is greater that 2? (b) What is the probability that the outcome of my experiment involves an even number and a coin toss resulting in heads? (c) Is it more likely to see an outcome involving a coin toss that resulted in heads, or an outcome involving a die roll less than 3 (d) What is the probabiltiy that the die roll portion of the experiment is greater than 7? 10. Let’s pretend that I’m actually an evil teacher and only give A’s to people who sit on the front row. If there are 40 people in a class, and 10 seats on the front row, how many different groups of A students could there possibly be? 3 11. Let’s pretend I’m even more evil, and actually give higher A’s to the students who sit further left on the front row (so 100 for seat 1, 99 for seat 2, and so on) and anyone not on the front row gets whatever grade they earned minus 10 (so no possible A’s). If there are still 40 students and 10 front row seats, how many different ways can I assign the coveted indivual A grades?