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Empirical probability measures the probability of an event by thought experiment.

But, by doing so, what information does it want to give? The experiment is done; so how can there be probability? The probability is found by the ratio of how many times the event has occured to total number of events. That's all! So, what does the assigned probability want to tell as the experiment is done already!?

Let $A$ be the required event. Now, experiment is performed $n$ times out of which $m$ times favoured $A$ . So,according to the definition, probability of A is $$P(A) = \dfrac{m}{n}$$ .

Probability gives the amount of certainty that A will occur before doing the experiment. But,here the experiment is done already(either in the thought or practically)! So, what does this empirical probability measure if the experiment is done already?? Confused. Please help.

  • To get a perfect value for a probability you would have to do infinitely many experiments, since a limited/finite number of experiments will always mean that you will have an uncertainty in the derived probability. This is also mentioned in you link. Could you maybe add which part of empirical probability you do not understand to you question? – fibonatic Jan 17 '15 at 01:23
  • @fibonatic: When does one guess or make a probability? Before performing the experiment,right? But the probability itself is measured by performing experiment! So, you want to ... –  Jan 17 '15 at 03:47
  • ...what will be the probability of heads before you toss a coin. But you find this by doing the experiment ie. Tossing the coin! So,what probability are you talking if you already tossed the coin? –  Jan 17 '15 at 04:06

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It means that if you do $k$ more experiments, as $k$ becomes larger, the number of times you get the $A$ result will approach $k P(A)$.

Brionius
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