If under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
P(A)= Number of times A occurred/Total number of Trials
Law of Large Numbers
The more times an experiment is repeated the closer the relative frequency gets to Classical Probability.
P(A)= Number of outcomes of A/Total number of Outcomes
The probability that events A or B will occur.P(A or B) = P(A) + P(B)- P(A and B)Keyword: OR
Mutually Exclusive
P(A or B) = P(A) + P(B)
Rule of Complementary Events
All events that do not include AP(A) + P(Complement of A)P(A) = 1-P(Complement of A)P(Complement of A) = 1-P(A)
Events happening togetherKeyword: ANDP(A and B) = P(A) * P(B)Conditional Probability-P(B given A) is read as "the probability of B given A"
Independent
The occurrence of A does not affect the probability of B.P(B Given A) = P(B)P(A Given B) = P(A)
Dependent
A and B are not IndependentP(A and B) = P(A) * P(B given A)P (A and B) = P(B) * P(A given B)
Probability of At least 1
P(at least 1___) = 1-P(O___)
The number of ways that two events can occur together of the first even can occur m ways and the second event can occur n ways is:m*n
Factorial Rule
The number of different permutations (order matters) of n different items when all n of them are selected is:n!
Combination Rule
The number of different combinations (order does not matter) when n different items are available, but only r of them are selected without replacements is:nCr
Permutation Rule
The number of arrangements when n different items are available but only r are selected:nPr