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Definition of probability:                                                 Probability is the the chance of occurrence of an event in the present or in future.When we  talk about the probability of  an event we basically mean the chance of the even. For example:                      when we want to know about the weather of our city.We are saying that  will it be sunny day or rainy day tomorrow.We are talking about the chance of rainy and sunny day.The chance of rainy or sunny is  50 50 .It may be possible that tomorrow will be a rainy day but it may be sunny.we can not say that it will be sunny.Because we do not know the exact condition. Another example:                            In the tossing of a cricket match.The probability of appearing of head or tail is 50 50. Both the team captains have a equal chance to win the toss. 

Matrices Multiplication.                                             Matrix multiplication is done in a very easy manner.In matrix multiplication we multiply the rows of the first matrix with the column of the second matrix.It is very important that the number of columns in the first matrix should be equal to the number of rows in the second matrix. Matrix addition:                        In matrix addition we add the first element of the first matrix with the first element of the second matrix,the second element of first with the second of the second and in the same manner we add the same position elements each other. Matrix subtraction:                                 Subtraction is also done in the same way as the addition is done.

Mode;           Mode is define as the most repeated value in the data set.We will take a sample of data and than find its mode. For example:                      1,3,4,5,6,7,8,6,4,5,2,3,4,6,5,4,5,6,5,7,5,8,6,7,5 So in this data 5 is repeated more than other values.So the mode for this data is 5. Range:              Range is define as the difference between the lowest value of the data and the highest value. For example we have the following data set.                                 {3,6,8,4,2.9} So,     Range=highest value - lowest value Here we have the highest value of the data is 9 and the smallest value is 2. Range=9-2           =7 hence the range for the above data is 7                    

Mean: Mean is usually known as average of data.Which is equal to the sum of total numbers divided by the total numbers. Now we interpret it mathematically by a formula. Mean=sum of total numbers ∕total numbers Now we have data as below.We want to find its mean.                          3,5,6,7,4,8,9,3,9 than the mean is,                            mean=3+5+6+7+4+8+9+3+9 / 9                        mean= 54/9                                  =6 so mean is 6 for the above data Median;              Median is the central value of the data.It mean the middle value of the date.There are two formulas to find the mean.First one is when the data is odd. and the second is when the data is even. Even and odd is decided on the basis of n.n is the total numbers. For odd data the formula is,                     Median=[(n+1)/2]th value.  Here n is total numbers. For even data we add the two middle values and divide it with 2. Let's take the following d

First we will find LCM of any two numbers. First of all what is LCM.LCM mean the least(smallest) common multiple.It mean the common number which divides the given numbers and is the smallest number greater than 1. For example: Find the LCM of  8 and 12  First find the factors of 8. 1✕8=8 2✕4=8 4✕2=8 8✕1=8 So the factors of 8 are 1,2,4,8 Now find the factors of 12. 1✕12=12 2✕6=12 3✕4=12 4✕3=12 6✕2=12 12✕1=12 So the factors of 112 are 1,2,3,4,6,12 Now factors of 8 and 12 are  Factors of 8.   1,2,4,8 Factors of 12. 1,2,3,4,6,12 So the least common multiple of 8 and 12 is 2. Now we will find the H.C.F. H.C.F stands for highest common factor.It means a number which is factor of the given numbers and is the largest number. Now let we take number 8 and 12 again.Now we will find their H.C.F. The factor of 8 and 12 are as follow Factors of 8.   1,2,4,8 Factors of 12. 1,2,3,4,6,12 The highest common factor of 8 and 12 is 4. In th

Some important Algebraic formulas for students. (x+y) 2 =x  2 +2(x.y)+y  2 In this formula we have all terms positive.The x and y terms which are first and last terms of the formula are square terms.The middle term is the two times of the  product of x and y. (x - y) 2 =x  2 -2(x.y)+y  2 In this formula  we have x and y terms are positive and square but the middle term is negative but its also two times of the product of x and y. (x  2_  y  2 ) =(x+y)(x-y) In this formula on left side of formula   x and y are square but square is not as a hole.So on right side we can write x and y in the product of (x+y) and (x-y). (x  2 +y  2 ) =(x+y)(x+y) In this formula we have both x and y are positive and square on lift side.So it is written as the product of (x+y) and (x+y). (x-y) 3 =(x  3 -3 x  2  y+3 x y  2 - y  3 ) In this formula on the right side the first and third terms are positive,the second and fourth terms are negative.The power of  X is reducing and

Type of matrices: There are many types of matrices which are described as below. Row matrix:                        A type of matrix in which only one row exist.The number of columns does not matters.Columns may be one or two or more than two. For example:                         ⟮1 5 7 9 ⟯  , ⟮2 1 3⟯ column matrix:                               A type of matrix  in which only one column exist.The no of rows does not matter.Whether they are one or two or three. For example:                        Rectangular matrix:                                       A type of matrix in which number of rows not equal to number of column.There may be 2 rows and 5 columns or 7 rows and 4 columns. For example: Square matrix:                             A matrix in which the number of rows are always equal to the number of columns. For  a square matrix it is important that the number of rows should be equal to the number of columns. For example: Diagonal

Difference between even and odd prime and rational  numbers. Even numbers:                              Even numbers are those numbers which can be divided by 2.For example 2,4,6,8,1000 200 250 are the example of even no which are completely divisible by 2. odd numbers:                           The numbers which can not be divided by 2 are called odd numbers.For example the number 3,5,7,11,21,33,99,9999,73 are odd because they are not divisible by 2. You can differentiate a number is odd or even you have to divide that no by 2.If it is completely divisible by 2 it means it is even.IF it is not divisible by 2 than its odd. Prime numbers:                               A prime no is a positive number greater than 1 that is divisible by itself or by 1. 1 is not a prime no because it has only one factor but prime numbers have two factors.For example 2,is divisible by 1 and 2 it self so 2 has two factors that are 1 and 2.but 1 has only 1 factor that is 1. Rational numbers

Difference between Micro economic and Macro economics. Macro economics.                               Macro economics looks at the economy as a whole or its major components of the economy.     For example:All consumers,Federal government,US economy Micro economics.                               Micro economics focuses on a specific economic unit.      For example: An individual household,firm or industry. Both individual and society face economic problems. Because They need to make choices because wants exceed needs. Example of economic problems faced by individual's and society's. Individual's economic problems. The budget line Society's economic problems. land. labor. capital. Entrepreneurial Ability.  FOR More information. visit YouTube.  https://youtu.be/VbAPerjhcR4 https://youtu.be/2ILYtQ_sHB4