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Sabtu, Desember 4

Probability


        

Branch of mathematics that discusses how to measure the level of confidence about the certainty will emerge whether or not an event called Compute Science Opportunities.
The origin of arithmetic this opportunity that is the question of a nobleman gambler named Chevalier de Mere to Blaise Pascal, about a problem of the distribution of money bet on a gamble if the game is stopped sebnelum completed. This question became the subject between Pascal and Fermat in their correspondence. From the brainstorming activity that is then arise branch of mathematics called Science Opportunities.
Because the birth of gambling tables, the explanation also often use dice and cards. For example, the dice, throw of the dice is called with an action, and of a series of actions carried out several times referred to as an experiment. There are no definite rules to answer the question how many possible outcomes of an experiment. In general, to find common approaches such as:
1.        Filling the space provided.
-        Multiplication rule:
-       The sum rule
Such as calculating the distance traveled from a town A to town B using several alternative roads.

2.       Permutation
Permutation is a different arrangement or sequence which is formed by some or all of the elements taken from a group of elements that are available. In general, we can say, "if there are k places available to be occupied by one of n elements, then the placement of elements into different places it can be done by:
                         (n) (n-1) (n-2) (n-3) ... (n-k +1)
Number of ways to place n items into k space provided is called permutation of k elements from n elements that are available and denoted as P (n, k) or nPk or P(n, k) or
, with k ≤ n.
If k = n then n element permutation of n elements that are available in summary called permutation of n and equal to:
                        P (n, n) = (n) (n-1) (n-2) (n-3) ... (1) = n!
Coat n! read n factorial.
Relation P (n, k) and P (n, n)
        P (n, n) = n (n-1) (n-2) ... (n-k +1) (n-k) ... (3) (2) (1) = n!
        P (n, k) = n (n-1) (n-2) ... (n-k +1)
By definition, (n-k) (n-k +1) ... (3) (2) (1) = n!
So,                  P (n, n) = P (n, k) x (n-k)!              or            P (n, k) =

                                                                                            P (n, k) =

3.       Combination
The combination of an accumulation of a group of elements or objects regardless of the arrangement or order, or so-called clustering or collecting also a number of elements.
The relationship between the combinations k of n elements C (n, k) with k permutations of n elements of P (n, k), namely:
C (n, k) x !                 = P (n, k)
C (n, k)          =

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