Question

5) Trace out the history of probability ?
6)approaches of probability ?
7)what is definite integration?
8)Distinguish between graphic solution and simplex solution

Answer 1

Answer:

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$5\: \mathfrak{question}- Trace \:out \:the \:history \:of \:probability ?$

$\mathfrak{5}$"A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat.

The concept of probability is an ambiguous one. It has gradually changed  content, and at present it has many meanings, in particular in the  philosophical literature. For our purpose it is suficient to distinguish between  two kinds of probability, each characterized by one of several adjectives,  depending on the context.

Objective, statistical, or aleatory probabilities are used for describing  properties of random mechanisms or experiments, such as games of chance, and for describing chance events in populations, such as the chance of a  male birth or the chance of dying at a certain age. Such probabilities are  derived from symmetry considerations or estimated from relative frequencies.  Based on an idealized game of chance with a finite number of equally possible  outcomes the classical probability or chance of a compound event is defined  as the ratio of the number of favorable outcomes to the total number of  outcomes.

$6\: \mathfrak{question}-approaches \:of \:probability ?$

$\mathfrak {6}$)There are three ways to assign probabilities to events:

classical approach,

relative-frequency approach,

subjective approach.

Classical Approach. . .

If an experiment has n simple outcomes, this method  would assign a probability of 1/n to each outcome. In  other words, each outcome is assumed to have an equal  probability of occurrence. This method is also called the axiomatic approach

Relative-Frequency Approach. . .

Probabilities are assigned on the basis of experimentation  or historical data.  Formally, Let A be an event of interest, and assume that  you have performed the same experiment n times so that  n is the number of times A could have occurred. Further, let nA be the number of times that A did occur.  Now, consider the relative frequency nA/n. Then, in  this method, we “attempt” to define P(A) as:

P(A) = lim n→∞  n A n

.

Subjective Approach. . .

In the subjective approach, we define probability as the  degree of belief that we hold in the occurrence of an  event. Thus, judgment is used as the basis for assigning  probabilities.

7)what is definite integration?

$\mathfrak{ 7 }$)The definite integral is defined to be exactly the limit and summation that we looked at in the last section to find the net area between a function and the x -axis. ... Collectively we'll often call a and b the interval of integration

8 Distinguish between graphic solution and simplex solution

$\mathfrak{ 8 }$ Difference between graphical method and simplex method under linear programming is given below

Explanation:

Graphical Method:

In graphical method it is  mandatory to finding the value of the objective function at each time of the vertex to getting the feasible region.  we prefer the graphical method when we have to find the solution of two decision variable .

Simplex method:  

In simplex method  we find the optimal value at the ending to getting the feasible region.  we prefer the simplex method when we have to find the solution of more then two decision variable .

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