Probability and Counting Chart

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Probability and Counting

Probability

Addition Rule

Mutural Exclusive?

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

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

Complement

"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 -)

Conditonal Probability

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

Mutiplication

Independent?

No

Dependent

Dependent: if A & B are not independent

-selection without replacement

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

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

Yes

Independent

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)

Classic and Realative Frequency Probability

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

Counting

Factorial Rule

n!

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

Fundamental Counting Rule

m * n

Combinations Rule

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

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

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.

Permutations Rule

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

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

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.