The probability calculus is the method through by it associated to each event a
number, called the probability of the event, that allows us to express quantitatively
the confidence degree on the happening of the event. There are several ways with
which it is possible to define the probability of an event. However, it will consider the
classic definition of mathematical probability, by Bernoulli and Laplace.
The definition of mathematical probability is useful to state some examples.
Considering the experiment "launch of two coins." It is a random experiment whose
possible results can be summarized "output" couples: "head- head," "head- cross"
and "cross- cross".
The probability of each of the three events can be gained by analyzing the possible
outcomes that the launch of the two coins can produce.
The possible results of the experiment are:
1 First launch: head/ second launch: head
2 First launch: head/ second launch: cross
3 First launch: cross/ second launch: head
4 First launch: cross/ second launch: cross
Of course, if the game is fair, that is, the coin is not soup up, the four possible
outcomes are considered equally probable, and thus each has probability of
occurrence of 25%.
Therefore, "head, head" and "cross, cross" are obtained each in correspondence of
only one of the possible results, respectively those shown in 1) and 4); instead of
"head, cross" and "cross, head" are obtained at the two possible outcomes 2) and 3).
So, we have three possible events related experiment "launch of two coins"
"Head, head" which has probability of happening equal to 25%;
"Cross, cross," which has probability of happening of 25%;
"Head, cross" that has probability of happening equal to 50%
So, if you were to bet on the results of "launch of two coins" would agree to bet on
the outcome "Head, cross."
The probability of an event, P(E), is the ratio between the number of favorable cases
and the number of possible cases, supposed all equally possible.
P(E)= (number of favourable cases)/ (number of possible cases)
-determining the number of all possible cases;
-determining the number of favorable cases, namely a situation that make the event
occurred for which you want to calculate the probability;
-calculating the ratio between the number of favorable cases and the number of
possible cases.
According to this definition, each probability is a number between 0 and 1. In addition,
the probability of an impossible event is 0 and the probability of a certain event is 1.
Example: throwing a dice, calculate the probability to obtain a number greater than
4. Note that in the roll of a dice you can get a number greater than 4 only if it comes
out 5 or 6, then we have 2 favorable cases while possible cases are 6 (six dice sides).
Therefore, using the above-mentioned formula we have: P(E)= 2/6= 1/3.