A probability is calculated or measured. It defines
the chance that an event has to occur.
Let's suppose that we have ten books: 7 of Mathematics and
3 of Physiscs, and we want to take one of them randomly. We assume that
the events "take a book" from the set are equiprobable,
that is all the outcomes have the same chance to be taken.
The event "take a Physics book" has three equiprobable results. Three
favorable outcomes (results) can occur among ten possibles
outcomes (results). the brobability to get a Physics book is then
Generally, in a random experiment associated to a sample space containing
N results mutually exlusive and equiprobable; if an event A has
nA favorable results, then the probability of the event A
denoted by P(A) is nA/N
The bprobability of the event A =
number of favorable outcomes/number of possibles outcomes
This definition works when the sample space is finite and contains
equiprobable results. When it is not the case, we use the experiment
process. We repeat the random experiment a lot of times, let's N times.
During all these N times, if we find nA events A, then the
probability of the event A is very close to nA/N, whish is
here the relative frequency of the event A. In the same
conditions, the more the number of trials is large, the more the relative
frequency is accurate and tends to a limite value which is the probability
of the associated event. This principle is called Bernoulli theorem
or law of the large numbers. This empirical definition of probability
is then the limite of nA/N when N tends to infinity (N very large).
Remark that N is said large when the relative frequency varies slowly
when passing from N to N+1.
When the sample space is continue, that is not countable, we define
probability by measurement. For example, when we throw a dart on a
cercle of radius R , the probability to get the dart inside a circle
of a radius r is the rate of the areas: πr2/πR2 =
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