Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Math Background Probability Introduction  
See also: random sampling, events and sample space  
Probability  IntroductionProbability is often used synonymously with "chance", "risk" or "odds", etc. The probability tells us how likely an event is. What are our chances of winning the lottery? What are the odds that we are hit by a hurricane ? What is the risk of this investment? Assessing and estimating the probability of an event is often very difficult. But in some very welldefined and simple situations, the probabilities can be assigned in a straightforward manner. When all outcomes of an experiment are of equal likelihood and when we know the sample space, then we can assign to each sample point a probability equal to 1/N, with N being the number of sample points. We can conclude this, since only one of the N outcomes is possible for each experiment.
For complex experiments, the number of sample points is often too large to be listed explicitly. We therefore need more sophisticated 'counting rules' for determining the number of sample points.
When we cannot rely on the assumption that all sample points are equally likely, we have to determine the probability of an event experimentally. We perform a large number of experiments N and count how often each of the sample points is obtained. The ratio of the number of occurrences of a certain sample point to the total number of experiments is called the relative frequency. The probability is then assigned the relative frequency of the occurrence of a sample point in this long series of repetitions of the experiment. This is based on the axiom, called the "law of large numbers", which says that the relative frequency approaches the true (theoretical) probability of the outcome if the experiment is repeated over and over again. Where n(E) is the number of times, the event E took place out of a total
of N experiments. From this definition we can see that the probability
is a number between 0 and 1. When the probability is 1, then we know that
a particular outcome is certain.


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