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Empirical Probability

The empirical probability, or probability, P (E), of an event E is the fraction of the number of times we expect E to occur.

Relationship to Estimate Probability :-
The estimated probability approaches the empirical probability as the number of trials gets larger and larger. Thus, estimated probability is an approximation, or estimate, of empirical probability. The larger the number of trials, the more accurate we expect this approximation to be.

If E consists of a single outcome, we refer to P (E) as the probability of the outcome ‘S’, and write P(S) for P (E). The collection of the probabilities of all the outcomes is the probability distribution.

Let n be the total number of trials. The empirical probability P(E) of an event E happening, is given by

P(E) =


Probability of an event can be any fraction from 0 to 1.

Probability of an impossible event is 0.

Probability of an event that is certain to occur is 1.

The sum of all probabilities is 1.

The probability of each event lies between 0 and 1.


1. Toss a fair coin and observe the uppermost side. Since we expect that head is as likely to come up as tail, we conclude that the empirical probability distribution is

P(H) =, P(T) =

2. Roll a fair dice. Since we expect to roll a "1" one sixth of the time,

P(1) =
Similarly, P(2) = , P(3) =, . . . , P(6) =

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