Introduction to Game-Theoretic Probability Assignment

Assignment Task

1. Consider the following problem: Alice and Bob, or A and B for short, design a game to be played with a fair six-sided die. The goal is to roll a 2 or a 5: whoever rolls one of those numbers wins the game. The players take turns rolling the die, player A goes first. They keep taking turns rolling the die until someone rolls a 2 or a 5. What is the probability that player A wins the game?

Below are ChatGPT’s attempts to solve this problem. All of them are wrong. For each solution, point out the flaw in logic that AI is making. 

2. In this task, you will create your own final exam question. Your submission should contain a question and a full solution. Here are some guidelines:

• You are to design a full answer (not multiple-choice) question. You can make up a hypothetical context or a computer science inspired one. Make sure you explain your set-up properly. Top points will be awarded for unique set-ups (some examples of these types of questions from the course include multiple factor authentication, Tower of Hanoi,). This website is useful for inspiration: Learning Journals also contain a ton of useful ideas and context examples.
• Your question should target topics directly from the course.
• Your question should contain a total of 3-5 parts targeting various concepts or aspects of the concept(s) you are trying to assess.
• Parts should be of varying difficulty: do not make 6 very easy questions that each require only one line of computation.
• Try out your question: it should lead to a meaningful learning experience, not just a simple.
• The questions should focus on the application of knowledge, not the recall of specific information. Do not include definitions or true/false questions. In your process of creation, think of proposing questions that test a variety of skills and contain “explain”, “how” and “why”.
• Solutions should include all the necessary steps laid out in a clear logical way. Designing questions is hard. But research shows that it improves learning.

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