My school has a research program and I potentially want to use this topic but I'm unsure if it can be answered with a simple response or if the question merits any research for that matter.
I want to try and figure out if the law of large numbers applies to events with individual/mutually exclusive outcomes. The law states as sample size grows, the mean tends to get closer to the average expected value, but does this same concept apply to events with independent outcomes such as fair coin tosses. Theoretically, I can toss a fair coin 100 times and get 100 heads. However seemingly improbable, still possible. I coin could be flipped ∞ times and get ∞ heads. This seemingly contradicts the Law of Large numbers. This is the topic I want to dive into. However, still being fairly new to probability, I'm unsure of the depth required or if this is even a question that merits research.
Feedback is appreciated.
*Undergrad
Edit: My question has been answered. There is no need for any new responses. However, if you want to, feel free.