The word probability is used to express uncertain events or knowledge, being closely related in meaning to *likely*, *risky*, *hazardous*, and *doubtful*. *Chance*,*odds*, and *bet* are other words expressing similar notions.

Probabilities are also thought of as numbers in a closed interval from 0 to 1 assigned to "events" whose occurrence or failure to occur is random.

The probability *P* of some event
*E *, denoted *P(E)*, is defined with respect to a sample space of all possible elementary events.

Probability *P(A)*, assigned to an event
*A*, is defined as the number of possible occurrences in *A*, as a ratio of the sample space.

Therefore;

*P(A) = N(A) / N(S)*

To determine the probability of an occurrence we need to define it with respect to a sample space of all possible elementary events.

Example:

If we define the probability of an even throw as the event, *E*, then;

*E = { 2, 4, 6 }*

If we define the sample space, *S*, as the total number of possible throws, then;

*S = {1, 2, 3, 4, 5, 6}*.

The probability of an even throw on a die is;

*P(E) = P(E) / P(S)*

*P(E)* = Number of even throws / Total number of possible throws

*P(E)* = 3/6 = 1/2.

Exercise:

In a single throw of a die, what is the probability of getting a number greater than four? Answer.

References:

Wikipedia. "Statistical Independence", Wikipedia Foundation Inc, "http://en.wikipedia.org/wiki/Probability", Last accessed 17th February 2006.

Arnold Mwesigye

Petrina Mangala