Probability and Counting

Counting

Permutations Rule

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Permutations are arrangements in which different sequences of the same items are counted separately

n! n1! n2!....nk!

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n!n1!n2! ...nk! = # of different permutations when 'n' items are available and all 'n' are selected without replacement, but some items are identical to others.

Combinations Rule

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Combinations -are arrangements in which different sequences of the same items are not counted separately.

nCr = n! / ((n-r)!r!)

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nCr = n! / ((n-r)!r!) = # of different combinations (order doesn't matter) when 'n' different items are available but only 'n' of them are selected without replacement.

Fundamental Counting Rule

m * n

Factorial Rule

n!

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n! = # of different permutations of 'n' different items when all 'n' of them are selected.

Probability

Classic and Realative Frequency Probability

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P(E) = # of ways E occurs/ total # of outcomes

Mutiplication

Independent?

Yes

Independent

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Independent: if occurance of events A and B does not affect the probability of the occurance of the other. - with replacement-5% rule

P(A) * P(B)

No

Dependent

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Dependent: if A & B are not independent-selection without replacement

P(A & B) = P(A) * P(B| A)

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P(B|A) = probability of event B occuring after event A

Conditonal Probability

P(B| A) = P(A & B) / P(A)

Complement

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"At least one" = one or more-complement of getting at least one particular event means that you get NO occurance of that event.P(A) and P(A -)

Addition Rule

Mutural Exclusive?

Yes

P(A or B) = P(A) + P(B)

No

P(A or B) = P(A) + P(B) - P(both)