Probability

Probability:

            Probability is the study of random or nondeterministic events.
  e.g.  if we toss a fair coin, then it results either a head or tail; of course we cannot be sure of the outcome in advance.
              N=the number of tosses
              n=the number of heads of obtained,
            P(n)=1/2

Statistical Experiment:

       A random or statistical experiment is one in which
i) all possible outcomes of the experiment are known in advance.
ii) A performance of an experiment results in an outcome which is not known in advance.
iii) the experiment can be repeated under identical conditions.

Sample space:

    The sample space of an experiment is the set of all possible outcomes of the experiment.

   e.g. if we toss a coin twice,the sample space will be 

        S={hh,ht,th,tt}

Event:

    A subset of a sample space is called an event. An event is said to occur if an element of the event occurs

   e.g. E={hh,ht}

Prob. of an event:

       If the sample space S is finite, the probability of an event A denoted by P(A) is defined as 

                              P(A)=size of A/size of S