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Statistics — Probability

Probability rules, distributions, and key theorems

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prob_and_stats 15 terms Feb 16, 2026
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Terms 15

1
Probability
Likelihood of an event occurring; between 0 and 1
2
Sample Space
Set of all possible outcomes of an experiment
3
Event
Subset of a sample space; one or more outcomes
4
Independent Events
Events where outcome of one does not affect the other
5
Mutually Exclusive
Events that cannot occur at the same time; P(A∩B) = 0
6
Addition Rule
P(A or B) = P(A) + P(B) − P(A and B)
7
Multiplication Rule
P(A and B) = P(A) × P(B|A); equals P(A)×P(B) if independent
8
Conditional Probability
P(A|B) = probability of A given B has occurred
9
Bayes' Theorem
P(A|B) = P(B|A)×P(A) / P(B); updates probability with new evidence
10
Binomial Distribution
Probability of k successes in n trials with probability p each
11
Normal Distribution
Bell curve; 68% within 1σ, 95% within 2σ, 99.7% within 3σ
12
Expected Value
Long-run average outcome; E(X) = Σ[x × P(x)]
13
Law of Large Numbers
As trials increase, sample mean approaches true population mean
14
Permutation
Ordered arrangement of items; nPr = n!/(n−r)!
15
Combination
Unordered selection of items; nCr = n!/[r!(n−r)!]