Probability Flashcards
(32 cards)
Relative Frequency Method
Numbers of times E occurs / total number of observations
Numbers of times E occurs / total number of observations
Relative Frequency Method
Permutation
Order matters- P = n! / (n-r)!
Order matters- P = n! / (n-r)!
Permutation
Combination
Order does not matter C = n! / r!(n-r)!
Order does not matter C = n! / r!(n-r)!
Combination
Complement Rule P(E) - P(EnF) =
1 - P(E) =
P(En~F) = P(E) - P(EnF) P(~E) = 1 - P(E)
P(En~F) =
P(~E) =
Complement Rule P(E) - P(EnF)
1 - P(E)
Addition Rule P(E) +P(F) - P(EnF) =
P(EuF)
P(EuF) =
Addition Rule P(E) +P(F) - P(EnF)
Multiplication Rule P(EnF) =
P(E) x P(F|E)
P(F) x P(E|F)
P(E) x P(F|E) =
P(F) x P(E|F) =
P(EnF) =
Proof Of Independent events
- ) P(A|B) = P(A)
2. ) P(AnB) = P(A) x P(B)
- ) P(A|B) = P(A)
2. ) P(AnB) = P(A) x P(B)
Proof Of Independent events
Conditional Probability of A, given B
P(A|B)
P(A|B) is a conditional probability for
A, given B
P(~A) x P(~B|~A) =
P(~A n ~B)
P(~A n ~B) =
P(~A) x P(~B|~A)
P(~A) x P(B|~A) =
P(~A n B)
P(~A n B) =
P(~A) x P(B|~A)
P(A) x P(B|A) =
P(A n B)
P(A n B) =
P(A) x P(B|A)
P(A) x P(~B|A) =
P(A n~B)
P(A n~B) =
P(A) x P(~B|A)
