Law of Large Numbers

Applet: Watch the convergence

Thought Experiment:
Consider tossing an fair coin several times. Think of the sequence of outcomes - each is Heads or Tails.
If you stop after one toss, what is your cumulative observed probability of heads? If you stop after two tosses, what is it? And continue.
Your friend is simultanously performing the same experiment. Do you expect she will get exactly the same sequence?

Applet: See two series here. When you open the applet, no tosses have been made. Click on the one toss button. To get the second toss, click on the one toss button again.
Keep doing that, looking at the tables at the bottom to see yours and your friend's results, and the graph at the top to see both the patterns for both of you.
Did they both converge to 0.5? (Which is what you expect for the probability of getting a Head when you toss a coin.)

Result: This illustrates that random events (such as the result of tossing a coin) have predictable long-term relative frequency. That is the value on the vertical axis that the graph converges to in the long run.

(When you rerun the applet, it will not always use an event like "Heads" in a fair coin. It will use different proportions to illustrate that the law is not dependent on the two outcomes being equally likely.)


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