Probabilità/Spazi di probabilità: differenze tra le versioni

===Counting Rules===

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:Example: Flip a coin three times, finding the number of possible sequences. N=3, K=2, therefore, KN =(2)(3)=6

 

:If K1, K2, ....KN are the numbers of distinct events that can occur on trials 1,....N in a series, the number of different sequences of N events that can occur is (K1)(K2)...(KN)

:Example: Flip a coin and roll a die, finding the number of possible sequences. Therefore, (K1)(K2) = (2)(6) = 12

:The number of different ways that N distinct things may be arranged in order is N! = (1)(2)(3)....(N-1)(N), where 0! = 1. An arrangement in order is called a permutation, so that the total number of permutations of N objects is N! (the symbol N! Is called N-factorial)

:Example: Arrange 10 items in order, finding the number of possible ways. Therefore, 10! = 10x9x8x7x6x5x4x3x2x1 = 3628800

 

:The number of ways of selecting and arranging r objects from among N distinct obejects is: N!/(N-r)! [nPr]

:Example: pick 3 things from 10 items, and arrange them in order. Therefore N=10, r=3, so 10!/(10-3)! = 10!/7! = 720

 

:The total number of ways of selecting r distinct combinations of N objects, irrespective of order (ie order NOT important), is: N!/r!(N-r)! [nCr]

:Example: Pick 3 items from 10 in any order, where N=10, r=3. Therefore, 10!/3!(7!) = 720/6 = 120