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ch29basicprobabilitylaws

ch29basicprobabilitylaws - Chapter29 Chapter29 A...

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Chapter 29:  Chapter 29:  Basic Probability Laws Basic Probability Laws A. A. Outcome Space and Events Outcome Space and Events Consider a random experiment such as the rolling of  Consider a random experiment such as the rolling of  a fair, ordinary die.  a fair, ordinary die.  The totality of all possible outcomes is called the  The totality of all possible outcomes is called the  outcome space outcome space  or the   or the  sample space sample space , denoted  , denoted  by  by  S S . . Let individual outcomes be  Let individual outcomes be  Then in set language, Then in set language, A subset  A subset  A A  of  of  S  S  is a partial collection of outcomes,   is a partial collection of outcomes,  and is called an  and is called an  event event . . , ....... , ........ , , 2 1 k e e e , ....... } , ........ , , { 2 1 k e e e S =
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For example, in the rolling of a fair dice, For example, in the rolling of a fair dice, A=Big={4,5,6} B=Even={2,4,6} C=Top={6} D=Small={1,2,3} E=Odd={1,3,5} Some terms: (i) Union event:  AUB[={2,4,5,6} Note:         = A or B or both } 6 , 5 , 4 , 3 , 2 , 1 { = S B A
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(ii) Intersection event: Note:             = A  and  B (iii) Sure event: S[={1,2,3,4,5,6} (iv) Impossible event:                the empty set (v) Complementary  event:  A‘=Non-A[=D] }] 6 , 4 { [ = B A B A {}] [ = φ
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(vi) Mutually exclusive  events: C and D are mutually  exclusive if  (vii)  Exhaustive events:                     are exhaustive events if (viii) Partition:  If                are mutually exclusive  and exhaustive, then they form a  partition of  S [e.g. B and E above] φ = D C k A A A , ........ , , 2 1 S A A A k = ........ 2 1 k A A A , ........ , , 2 1
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B. Probability and Probability Laws B. Probability and Probability Laws Suppose                      is an event.  Then, whenever one of these elements turns up, we say that  A  has  occurred. For example, in a game of mahjong, you are “calling” for a 2-,5-, or 8- circle. Then the event A={2,5,8} is your  bingo event. Whenever, any one of these turns up, the bingo event is achieved. Naturally, when we are interested in a particular event,  A,  we would like  to know the  chance  (i.e.  probability ) that  will occur.  If  has more elements  (i.e.       =big),  then the chance will be bigger.  Otherwise, it will be smaller.  Hence it is natural to define the probability of A to be } , ........ , , { 2 1 A N e e e A = A N N N A P A = ) (
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