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Probability (5)

Pe ne general multiplication rule pe and f pe pf

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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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