peluang (matematika)

Opportunity, Permutations & Combinations Mathematics
Web Formula Opportunities collecting materials, Permutations & Combinations Mathematics for high school kids to UAN SNMPTN SNCA SIMAK UI. Please learn :)
1) PermutationsPermutation is an arrangement of different elements in a specific order. On the permutation sequence noted thatPermutations of k elements from n elements are all different possible sequences of k elements taken from n distinct elements. Many permutations of k elements from n elements written or.Cyclic permutation (circular) of n elements is (n-1)!How quickly do the problems of permutations

    with NPK writing, arithmetic 10P4
    we immediately write 4 points from 10 backwards, ie 10.9.8.7
    10P4 = 10x9x8x7 so how is it? count yourself :)
Examples of cyclic permutations:

    A family consists of six people sitting around a circular table. How many ways so that they can sit around the table in a different way?
    Answer:
    The number of ways that 6 people can sit around the table in a different order with many permutations cyclic (circular) 6 elements, namely:
2) CombinationThe combination is an arrangement of elements with no regard to the order. In combination AB = BA. Of a set with n elements can be assembled with a set of parts for each subsets with k elements of a set with n elements is called a combination of n k elements are denoted by,
Example:Given the set.Determine many subsets of the set A which has 2 elements!Answer:
Many subsets of A which has 2 elements is C (6, 2).

How quickly do the problem combination

    with writing NCK, count 10C4
we immediately write 4 points from 10 back and then divided by 4!, which divided 10.9.8.7 4.3.2.1so 10C4 = 10x9x8x7 / 4x3x2x1 how much is it? count yourself :)
Ohya if asked the same 10C6 10C4, 10C6 = 10C4 remember. other examples20C5 = 20C153C2 = 3C1100C97 = 100C3see the pattern? hehe hopefully useful!Math Opportunities
1. Definition of Sample Space and EventsThe set S of all events or events that may appear from an experiment is called the sample space. Specific incident or an element of S is called a point sample or samples. An event A is a subset of the sample space S.

    Example:
    Given experiment throwing three coins at once one time, each of which has the number (A) and drawing (G). If P is the incident came two figures, set S, P (event)!
    Answer:
    S = {AAA, AAG, AGA, GAA, GAG, AGG, GGA, GGG}
    P = {AAG, AGA, GAA}
2. An Opportunity Understanding GenesisIn an experiment there are n possible outcomes and each had the opportunity to come together. If the results of this experiment, there are k outcomes of event A, then the chance of event A written P (A) is determined by the formula:

    Example:
    In throwing a dice experiment, determine the incidence of experimental opportunities arise even number!
    Answer: S = {1, 2, 3, 4, 5, 6} then n (S) = 6
    Let A be the event appear even number, then:
    A = {2, 4, 6} and n (A) = 3
3. Opportunity Value range MathematicsLet A be any event in the sample space S with n (S) = n, n (A) = k andSo, the odds of an event lies in the closed interval [0,1]. An event called the impossible event zero chances and the chances of events called the incident one for sure.
4. Frequency of Hope A GenesisIf A is an event on the frequency of the sample space S with a chance of P (A), then the expected frequency of n times the event A trial is nx P (A).

    Example:
    When a dice 720 times, what is the expected frequency of the appearance of the dice 1? Answer:
    In throwing dice 1 time, S = {1, 2, 3, 4, 5, 6} then n (S) = 6.
    Let A be the incidence of emergence of the dice 1, then:
    A = {1} and n (A) so that:
The frequency of emergence hope dice 1 is
5. Complement An Opportunity GenesisLet S be a sample space with n (S) = n, A is incident on the sample space S, with n (A) = k and Ac is the complement of event A, then the value of n (Ac) = n - k, so that:
So, if the chance result of an experiment is P, then the chances of it not happening result is (1 - P).Genesis Compound Opportunity
1. Combined Two EventsFor any events A and B apply:
Note: read "Genesis A or B and read" The events A and B "

    Example:
    In throwing a dice, A is a composite number and appearance of event B the event appear even number. Look for a chance of event A or B!
    Answer:
2. The events Mutual ReleaseFor each event applies if. So in this case, A and B are called independent of the other two events.
3. Conditional GenesisIf P (B) is a chance event B, then P (A | B) is defined as the chance of event A condition that B has occurred. If you are the chances of A and B, then in this case, the two events are not independent.
4. Bayes TheoremBayes Theorem (1720 - 1763) put forward the relationship between P (A | B) and P (B | A) in the following theorem:
5. Genesis independent Stokhastik(I) Suppose A and B are events - events in the sample space S, A and B are called the two events are independent if the occurrence stokhastik not influenced one another or appearance: P (A | B) = P (A), so that:Distribution Opportunities
1. Definition of random variables and distribution opportunities.Random variable X is a function of a sample of S into the real numbers R. If X is a random variable on a sample space S premises X (S) is a finite set, a random variable X is called discrete random variables. If Y is a random variable on a sample space S with Y (S) is an interval, a random variable Y is called continuous random variables. If X is a function of the sample S to the set of real numbers R, for each and every then:
Suppose X is a discrete random variable on a sample space S, the distribution function of future opportunities shortened odds of X is a function f of R which is determined by the following formula:
2. Distribution BinomBinomial Distribution Binom or expressed by the following formula:

With P as a parameter andThe formula is expressed as:for n = 0, 1, 2, .... , NWith P as a parameter and
P = chances of successn = Many trialsx = Appears Successfuln-x = Appears to fail