Empirical Law of Large Numbers
When tossing a coin, there are two possible outcomes: heads or tails.
Since the mathematical probability of an event is the ratio between the number of favorable cases and the number of possible cases, both the event ‘heads occurs’ and the event ‘tails occurs’ have probability 1/2.
Another way to measure the probability of an event is empirical: the trial is repeated several times, and the relative frequency of the event is calculated. This is the ratio between the number of times the event occurs and the number of trials performed.
Use the app below to observe how, as the number of trials increases, the value of the relative frequency of an event approaches the mathematical probability of the event.
Food for Thought...
You have a bag, containing a red marble and a blue marble. You pick one of the marbles from the bag, take note of its color, and put the marble back in the bag. What is the probability to extract a blue marble? By repeating the experiment over and over, can you say that the empirical law of large numbers holds? Explain your conjectures.
You now have a bag containing a red marble, a blue marble and a yellow marble. You pick one of the marbles from the bag, take note of its color, and don't put the marble back in the bag. What is the probability to extract a blue marble? By repeating the experiment over and over, can you say that the empirical law of large numbers holds in this case? Explain your conjectures.