Your paper should be approximately 3 pages double spaced (~750-1000 words).
Papers can talk directly about a mathematical topic related to probability, they can be a personal reflection, and an expository talk relating approximation to something in history, design, culture…you name it! Above all, make sure your writing is focused and specific. However, if an approximation appears in your paper, write about it with as much precision as you can.
A good paper should include a working definition of probability that is relevant to your topic, a small computational example, and outside references. Good papers are readable (avoid typos and grammatical mistakes).
Avoid a paper that is a simple laundry list of approximation problems in your life. Write about something you find interesting or that you care about. Try to find a way to quantify the approximation problem that you want to discuss. Looking for interesting approximation mistakes is often very insightful.
I will grade your paper on a 0-5 point scale. Papers that receive a 5 are exceptional. Note that the grade on your short papers represents a pretty hefty chunk of your overall grade (40%). In the grade book these assignments are not weighted as they will be when I compute your grade. Blowing off your papers is a really bad idea! Treat this assignment with the same seriousness that you would a test.
Enhancing Weather Information with Probability Forecasts – American Meteorological Society (ametsoc.org)
How to Calculate Probability for Weather (sciencing.com)
Tips for the last paper: You picked a good topic, but you didn’t tell me precisely how approximation was used in the Covid pandemic. Maybe focusing on the covid pandemic as a whole was too broad, and it would have been better to focus on a specific type of approximation. For example, how do we approximate infection rates or death rates?