# Your code hereHomework 1
BSTA 550
Assignment information
Directions
Please turn in this homework on Brightspace. Please submit your homework as a pdf or html file. You can type your work in this file and render it, or submit a single file with photos of your written work or any other method that can be turned into a pdf. Please let me know if you prefer to submit a physical copy, we can arrange for a physical “turn in” during Monday’s class.
You must show all of your work to receive credit.
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NoteAI Use Statement
Using AI is not required in this class. If you did use an AI tool (ChatGPT, Claude, Copilot, Gemini, an RStudio assistant, etc.) on this homework, add a brief AI Use Statement at the very top of your submission. Include:
- Which tool(s) you used
- What for (a sentence or two, with question numbers)
- Where it contributed to any written interpretations (if at all)
- You do NOT need to link your conversation.
For example:
AI Use Statement: Claude was used to explain an error message in Question 3. All statistical reasoning, code review, and conclusions are my own.
OR
AI Use Statement: AI was not used in this assignment.
Before using AI, check the table of allowed uses in the Generative AI Policy. For homework, AI can help you understand (explain an error or a concept, check an answer you already worked out, give feedback on your own writing), but it should not do the problem for you. A half-finished answer that shows your thinking is always better than a polished one from AI!
Questions
1. Outcomes, events, and sample space
In the below parts, please list (i) one specific outcome, (ii) one event that contains more than one outcome, and (iii) the sample space.
Part a
Chris has a 5-pack of Gatorade sports drink: 1 orange, 2 lemon-lime, and 2 fruit punch. He blindly grabs one out of the pack over and over if necessary, without replacement, until he finds an orange one. Note, each lemon-lime is indistinguishable, and each fruit punch is indistinguishable.
Answer:
- One outcome:
- One event:
- Sample space:
Part b
A claw machine contains 10 plush toys: 5 Red Squishies (R), 3 Blue Dinosaurs (B), and 2 Yellow Star Puffs (Y). You successfully grab a toy, remove it, and then grab a second toy (sampling without replacement). The result is the ordered pair of the two toys’ colors.
Answer:
- One outcome:
- One event:
- Sample space:
Part c
You are opening a series of mofusound Cat blind boxes. There are 4 possible figurines to collect: 1 shark cat (S), 1 orange striped fish cat (O), 1 hen cat (H), and 1 cow cat (C). You buy a single blind box.
Answer:
- One outcome:
- One event:
- Sample space:
2. Running a simulation!
This assignment requires you to use the four-step simulation process in R to approximate the probability of a specific event.
Scenario: The Mystic Orb Blind Boxes
The “Mystic Orb” collectible series has 5 total figures you can find in the blind boxes:
- 1 Rare Mystery Toy (M) - The figure Nicky wants.
- 4 Common Figures (C) - All other figures.
When you buy a blind box, you receive one of the 5 figures, and each figure is equally likely.
Nicky decides to buy three Mystic Orb blind boxes. She really wants to get the Rare Mystery Toy!! The random variable of interest is X, the number of boxes out of the three that contain the Rare Mystery Toy.
Using the four-step simulation process, approximate the probability that Nicky gets at least one Rare Mystery Toy when she buys three boxes.
Answer: