3-1 Overview
● Rare Even Rule for Inferential Statistics: if under a given assumption, the probability of a
particular observed event is extremely small, we conclude that the assumption is probably
not correct
3-2 Fundamentals
● An event is any collection of results or outcomes of a procedure
● Asimple event is an outcome or an event that cannot be further broken down into simpler
components
● The sample space for a procedure consists of all possible simple events. That is, the
sample space consists of all outcomes that cannot be broken down any further
● Notation for Probabilities:
○ P denotes a probability
○ A, B, and C denote specific events
○ P(A) denotes probability of eventAoccurring
● Relative FrequencyApproximation of Probability:
○ P(A) = number of times A occurred / number of time trial was repeated
○ When finding probabilities with this, we obtain an approximation instead of an
exact value; as total number of observations increases, approximation tends to get
closer to actual probability
● ClassicalApproach to Probability (Requires Equally Likely Outcomes)
○ P(A) = number of ways Acan occur / number of different simple events
○ P(A) = s / n
● Subjective Probabilities: P(A), the probability of eventA, is estimated by using
knowledge of relevant circumstances
● Law of Large Numbers: as a procedure is repeated again and again, the relative frequency
probability of an event tends to approach the actual probability
● The mathematical probability of any event is 0, 1, or a number in between
○ probability of impossible events is 0
○ probability of certain events is 1
○ For any event, probability ofAis 0<= P(A) <= 1
Complementary Events
● The complement of eventA, denoted byAbar, consists of all outcomes in which eventA
does not occur
3-3 Addition Rule
● P(Aor B) is the probability that either eventAoccurs or event B occurs, or they both
occur
○ the word ‘or’in these cases is used inclusively which mean either one or the other
or both
● Acompound event is any event combining two or more simple events
● When finding probability that eventAoccurs, or event B occurs, find the total number of
ways Acan occur, and the number of ways B can occur, but find that total in such a way
that no outcome is counted more than once
● FormalAddition Rule: P(Aor B) = P(A) + P(B) - P(Aand B)
● IntuitiveAddition Rule: To find P(Aor B), find the sum of the number of ways eventA
can occur and the number of ways B can occur, adding in such a way that

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