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... • If a finite set A is a union of k mutually disjoint sets A1, A2, …, Ak, then n(A) = n(Ai) • Number of words of length no more than 3 • Number of integers divisible by 5 • If A is a finite set and B is its subset, then n(A – B) = n(A) – n(B) • How many students are needed so that the probability o ...
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... number and event B is to spin an odd number, are these events compatible or incompatible? b) If Qi wants to determine the probability of spinning this spinner two times and landing on 1 and then 2, would the two spins be dependent events or independent events? c) If Event C is landing on 1 or 2, wha ...
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... with the de nition of random occurrences. Criteria for random occurrences to be Poisson distributed are presented and followed by a discussion of Poisson stochastic processes and their generalizations. Examples cover simple applications of the compound Poisson processes in biological modeling. ...
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6.4: Type I and Type II errors Type I error : Reject r0

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Diego Mendoza Learning Progression
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... After using the multiplication rule, students should conclude that the probability that an introductory statistics student who gets an A, B, or C studies at least six hours a week and belongs to a study group is 31.5%. Although it is given in the question, a note should be given that P(B|A) is the s ...
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Conditional Probability

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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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