Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 11 – Probability Applets Lab

Wiki Page
2026-01-17T21:14:47-08:00

Question: Which provides a better estimate of the theoretical probability P(H) for the unfair coin: an empirical probability using 30 flips or 1000 flips? Why do you think so?

We expect the empirical probability from a 1000 flips to give a better estimate.

Why?

When we examine empirical probabilities, on average they do a good job estimating a theoretical probability. We can see this in the graphs. The mean of the empirical probability estimates is pretty close to the theoretical probability with both the fair coin and the weighted coin.

However, there is less variability in the empirical probabilities with a 1000 flips compared to 30 flips. In other words, with 1,000 flips the empirical probability estimates tend to be closer to the theoretical probability. Therefore, 1,000 flips is more likely to give a better estimate than 30 flips.