They are both branches of mathematics.
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There is no relationship between sequences and probability.
What is the symbol for a Probability of success in a binomial trial?
There is no direct relationship between degrees of freedom and probability values.
They are the same. The full name is the Probability Distribution Function (pdf).
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.