Statistics for Decision- Making in Business - Maricopa Community ...

There is less than a 1% chance that both contaminated bushels went out.
Does this outcome satisfy the farm producing these bushels of corn Thinking in more detail, the
main concern is actually in regards to one or more (at least one) contaminated bushel going out!
In order to address how to find this, it is useful to think about the following, perhaps obvious,
characteristic.
Basic Properties of Probability (Kolmogorov Axioms)
1) A particular event is: guaranteed to not occur, is guaranteed to occur, or lies somewhere
between these extremes.
2) In a given situation, or sample space, the likelihood of something occurring (however
small or insignificant), is guaranteed.
3) The summed probabilities of all the possible events in a situation constitute the entire, or
the whole of all possibilities.
Mathematically, suppose that a sample space consists of n events
above verbal rules translate into:
. Then, the
1) For any arbitrary event between events 1 and n, let‟s call this event , then:
( )
2) Using to denote the sample space,
( )
3) Summing the probabilities gives 100% of all possible outcomes:
( ) ( ) ( ) ( )
These basic properties are often referred to as the Kolmogorov axioms, named after the
mathematician Andrey Kolmogorov. An axiom can be thought of as a necessary assumption. For
instance, when physicists develop new concepts in physics, they assume that gravity follows
certain properties. Thus, they have gravity axioms.
The Kolmogorov axioms are extremely important in probability and the development of new
ideas.
Statistics for Decision-Making in Business © Milos Podmanik Page 93