Mathematical probability is how many times something is projected to occur, where as experimental probability is how many times it actually occurred.
For example, when discussing the probability of a coin landing heads side up...
Mathematical probability is 1:2.
However, if you actually carryout an experiment flipping the coin 5 times the Experimental probability may be 2:5
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Probability is more of a mathematical statisic whereas chance is more of luck or fortunance.
They are exactly the same
They are probabilities: that is, estimates of the likelihood of an event happening.
Boolean Algebra is the study of the algebra of logic whilst Mathematical logic is a way of applying Boolean algebra. Other applications include set theory, digital logic and probability.
The difference between "at least" and "at most" is not restricted to probability. The difference is simply one between the precise meaning of the phrases in every day English language.