Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, moment generating functions, law of large numbers, ...

"Yes or no: was there once life on Mars?" I can't say. "What about intelligent life?"' That seems most unlikely, but again, I can't really say. The simple yes-or-no framework has no place for shadings ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

Probability is the theory that allows us to make an inference from a sample to a population. It provides the mathematical and theoretical basis for quantifying uncertainty. Probability is also used ...

a priori Probability: the probability that we determine from knowing the process by which the uncertain event happens (by logically examining existing information). Certain Event: event that is sure ...