Unformatted text preview: F  E) = P(F and E) N(F and E)
=
for any two events E and F.
P(E)
N(E) General Multiplication Rule – P(E and F) = P(E) × P(F  E) if E and F are any two events
Alternative Definition of Independent Events – two events E and F are independent if
P(E  F) = P(E) , which is equivalent to P(F  E) = P(F)
Multiplication Rule of Counting – the total number of choices for a task involving a sequence of
subtasks having c1, c2 , c3, ... options, respectively, is c1 ! c2 ! c3 ! ...
If an outfit can be created using any of two different hats, four different jackets, and three different
pants, then 2 · 4 · 3 = 24 different outfits can be created.
Permutation – an ordered arrangement of objects
Factorial  n! = n ! (n " 1) ! ... ! 2 !1 NOTE: 0! = 1 and 1! = 1
The number of arrangements of 5 people in a line is 5! = 5 · 4 · 3 · 2 · 1 = 120. Permutations of n distinct objects taken r at a time (repetition of objects is not allowed) –
n Pr = n!
n " (n ! 1) " ... " 2 "1
=
= n " (n ! 1) " ... " (n ! r + 1)...
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 Spring '14
 Probability, Probability theory, 48 52

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