Best Way to Learn Probability

Introduction best way to learn probability:

The theory of best way of probability begins to develop for study of games of chance such as roulette and cards. The best way of probability used for not only games, probability also prevails in other walks of life such as commerce, financial system, and even in day-to-day daily activities. Systematic method for probability theory was introduced by French mathematicians Blaise Pascal and Pierre. In this article we shall discuss best way to learn probability with example problems.


Learn probability formula with example problems


Learn probability formula:

Probability P(E) =        Number of way the event happen
The total number of possible outcome of an event

Example 1: A spinner has 5 equal sectors colored blue, white, green, orange and red. Spinning the spinner, Find the probability of leading green color?

Solution:

The possible outcomes of these events are blue, white, green, orange and red.

P(green) = Number of way land green
Total number of colors

= `1/5.`

Example 2: A six sided unbiased die is rolled. Find the probability getting one? Find the probability of an even number rolling?

Solution:

P(E)  = Number of way to get a one
Total number of sides

P(getting number 1)    = 1.

Total number of sides = 6

Therefore probability   = `1/6.`

Example 3: A six sided unbiased die is rolled. Find the probability of an even number rolling?

Solution:

P(E)= Number of way to get even number
Total number of sides

P (getting even number) = 3.

Total number of sides    = 6

Therefore probability      = 3/6 = 1/2

Example 4: If a1 and a2 are two events related with a random experiment such that P(a2)=0.45, P(a1 or a2)= 0.75 and P(a1 and a2)=0.25, Calculate P(a1).

Solution:

Let P (a1) = x then,

P (a1 or a2) =P (a) + P (a2) – P (a1 and a2)

= 0.75 = x + 0.45 – 0.25

Sum the experiment value

x = (0.75-0.45 + 0.25) = 0.65

Hence P(a1) = 0.55.

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Learn probability with practice problem


Problem 1: A six sided unbiased die is rolled. Find the probability of an odd number rolling?

Answer: `1/2`

Problem 2: A spinner has 4 equal sectors colored blue, white, green, and orange. Spinning the spinner, find the probability of leading white color?

Answer: `1/4.`

LCD and LCM in Math

Introduction to math lcd and lcm:

In math, the lcd and lcm are terms used to perform the arithmetic operations in fraction. Expansion of lcd is least common denominator and expansion of lcm is least common multiple. Both are same in basic idea. The least common denominator is least denominator value in fraction addition. The least common multiple is a small number and it is divisible by all factors of number. The lcm s used in least common denominator calculation. The lcm is determined by the factorization method that is list out the multiples of number and find out the least value. Both lcd and lcm are defined in algebra math. We can get the detail description for least common denominator and least common multiple with example from online articles and tutorials.

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Math lcd and lcm


Least common multiples in math:

We can use the two methods for least common multiples determination.

Method 1:

List out the multiples of each numbers.
Find out the least value in that multiples.
Method 2:

List out the prime factors of each numbers. (For example, 6 – 2 x 3 and 12 – 2 x 2 x 3).
Count how many number of prime factors in each factorization. (Prime number 2 counts are three and prime number 3 count is 3).
Select the large count prime number. (2 x 3 x 2)
Multiply the selected prime numbers.(12)
Least common denominator in math:

The steps for least common denominator are same as above. Only difference is the value in fraction denominator.

Multiples of each number is listed.
Find the smallest number in multiples.

Example problems for lcd and lcm


Example 1: Find out the least common denominator of `2/6` and `1/18`

Solution:

Step 1:

Given fraction values are `2/6` and `1/18`

Step 2:

Find the multiples of numbers 6 and 18.

Multiples of number 6 is 12, 18, 24, 30….

Multiples of number 18 is 36, 54, 72…

Step 3:

Smallest number in list of multiples is 18.

Step 4:

The least common denominator of `2/6` and `1/18` are 18.

Example 2: Find out the least common multiple of 4 and 8.

Solution:

Step 1:

Given values are 4 and 8.

Step 2:

Find the multiples of 4 and 8.

Multiples of number 4 is 8, 12, 16….

Multiples of number 8 is 16, 24, 32…

Step 3:

Smallest multiple in list is 16.

Step 4:

The least common multiple of 4 and 8 is 16.

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Practice math problems for lcd and lcm:
1. Find out the least common denominator of `1/2` and `1/10` .

Solution: The least common denominator is 10.

2. Find out the least common multiple of 3 and 9.

Solution: The least common multiple is 9.

Study Learn Division

Introduction of study learn Division:
Study learns Division is the inverse of multiplication in the mathematics operation. It determines the how many times 1 value is consist of other. It can be expressed as x/0.where x is the dividend. Depends upon the arithmetic setting a well defined value can be assigned to the expression. Having problem with Examples of Rational Numbers keep reading my upcoming posts, i will try to help you.

We write division of 2 numbers as a/b, where a is the dividend and b is the divisor.

The division of 2 rational numbers, where the divisor is not equal to zero, results in another rational number.


Basic properties of study learn division:

A number which is divided by it is equal to 1.

A number which is divided by one is equal to the number itself.

Zero divided by anything is equal to zero. It is known as zero property.

Any number divided by 0 is undefined.


Example of study learns division:


1.To solve for dividing 8/4

Sol:

8/4=2

8 divided by 4 equal to 2

The answer is 2

2. To solve for dividing 12/6

Sol:

12/6=2

12 divided by 6 equal to 2

The answer is 2

3. To solve for dividing 5/2

Sol:

5/2 = 2.5

5 divided by 2 equal to 2.5

The answer is 2.5

4. To solve for 100/50

Sol:

100/50=2

100 divided by 50 equal to 2

The answer is 2

5. To solve for 50/2

Sol:

50/2= 25

50 divided by 2 equal to 25

The answer is 25

6. To solve for 100/25

Sol:

100 divided by 25 equal to 4

The answer is 4

7. To solve for 500/100

Sol:

500/100=5

500 divided by 100 equal to 5

The answer is 5

8. To solve for 1000/100

Sol:

1000/100=10

1000 dividing 10 equal to 10

The answer is 10

9. To solve for 500/50

Sol:

500/50=10

500 divided by 50 equal to 10

The answer is 10

10. To solve 1000/500

Sol:

1000/500=2

1000 divided by 500 equal to 2

The answer is 2

11. To solve for 15/5

sol:

15/5 =3

15 divided by 5 equal to 3

The answer is 3

12. To solve for 45/5

Sol:

45/5 =9

45 divided by 5 equal to 9

The answer is 9

Vriable of Math

Introduction to variable of math:

A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e. completely fixed or fixed in the context of use. The concepts of constants and variables are fundamental to all modern mathematics, science, engineering, and computer programming. Please express your views of this topic Functions Math by commenting on blog.


Example problems of variable in math:


Variable of math problem 1:

James, Mickel and John are friends. James’s age is one-third of Mickel and John is five years elder than Mickel. If the sum of the age of the friends is 40, find the ages of each one.

Sol:

From the statement,

Age of Mickel= x

Age of James   `=x/3 `

Age of John = x+5

Sum of the ages=40.

`x/3 + x+x+5= 40`

`(7x+15)/3 =40`

Multiplying by 3 on both sides,

7x +15=120

Subtracting 15 on both sides,

7x=105

Dividing by 7 on both sides,

x=15

Therefore, age of James=15/3=5

Age of Mickel                 =15

Age of John                  =15+5=20

Variable of math problem 2:

Solve the following system:

x + y = 20

2x - y = 10

Sol:

We cay solve x aid y by using substitution method.

Given         x + y = 20……………. (1)

2x - y = 10……………... (2)

Solve the equation (1) for y,

x+ y= 20

Subtract to the value x on both sides,

y= 20-x ………. (3)

Substitute the value y into the second equation. They we get,

2x-(20-x) =10

2x-20+x=10

3x-20= 10

Add to the value 20 on both sides.

3x-20+20= 10+20

3x= 30

Divide by the value 3 on both sides.

x=10

Substitute the value of x into the equation (1).

10+y=20

Add the value -10 on both sides.

y= 20-10

y=10

Answer: x=10 and y=10

Variable of math problem 3:

Solve the equation 7(-5b - 3) - (5b - 4) = -6(4b + 6) + 3

Sol:

Given the equation 7(-5b - 3) - (5b - 4) = -6(4b + 6) + 3

First we can multiple the factor variables for both left and right hand side.

-35b - 21 - 5b + 4 = -24b - 36 +3

Here we can group the like terms on both sides.

-40b - 17 = -24b – 33

Add 20b+15 on both sides.

-40b-17+24b+33=0

-16b+16=0

Subtract 16 on both sides.

-16b= -16

Divide -16 on both sides.

`b= (-16)/-16`

` = 1`

Answer: b=1

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Practice problems of variable in math:


Find x: 5x+3x-6=74
Solve: 3(y -3) + 5z - 4(y -2z -3) + 8
Answer:

x= 10
13z-y+11

Math Division 10

Introduction math division 10:

In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication.

Specifically, if c time’s b equals a, written:

`c * b=a`

Where b is not zero, then a divided by b equals c, written:

`a/b=c`

For instance,

`6/3=2`

Since

`2*3=6` .

In the above expression, a is called the dividend, b the divisor and c the quotient.

Source Wikipedia

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Math division 10 explanations:


Here we will see math division based on divisor 10

Example1:

The division process in based on divisor 10 is very simple to divide any number

50 apples to give 10 apples for each member how many members got this apple to find the answer for this problem?

Solution:

Step 1: the total number of apple is 50

Step 2: to give 10 apples for each member

Step 3: divide `50/10` we got the answer for this problem

10 ) 50 ( 5                              `5 *10=50`

50

----------

0

----------

Quotient is `5 ` the remainder is `zero`

We give `50 ` apples to `5 ` people

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Math division 10 practice problems:


Here we will learn about how to do the math division problem based divisor 10

Example1:

The ramu in hand 230 balls to fill in the bag. The each bag to cover only ten balls .to finds how many bag to need for fill the all balls?

Solution:

Step 1: the total number of balls `230`

Step 2; one bag contain ten balls

Step 3: to find how many bags to fill all balls

10 ) 230 ( 23

20

--------------

30

30

------------

0

------------

Example2:

In the each boat cover 10 peoples .the 12495 number of people in near the river   to cross the river in this side to another side. Find how many boats need for they are cross the river?

Solution:

Step 1; the total number of people in near the river `12495`

Step 2: the each boats cover 10 number of people

Step 3: to solve this problem to find the needed boats

3) 12495 (1249

10

-----------

24

20

-----------

49

40

-----------

95

90

-----------

5

------------

Quotient is `1249 ` and Remainder is `5 ` so, we arrange one boat for `5 ` member

Needed boats for they are cross the river = 1250

Dividing Radicals

Radicals in algebra are defined as the roots of a number or a variable. It is denoted with a symbol like v. The number which is mentioned in the ‘v’ portion of the symbol is called as the index of the symbol and the number or the variable or an expression entered inside the symbol is called radicand.
The meaning is that if the radicand is multiplied by itself index number of times, the product is the number that represents the radicand. If the index is 2, then the radical is called a square root and if the same is 3, then it is referred as cube root.

Usually for square roots, the index 2 is not mentioned. Thus radicals a type of expressions and like any other expression they can also undergo basic operations.
A radical can also be expressed in equivalent exponential form, with a rational exponent.. In general, nth root of am is equivalent to am/n. This concept is used in dividing radicals with variables. For example, (x^2)/v(x) can be simplified as (x^2)/(x1/2), which is, as per exponential rules is equal to (x3/2). This can be switched back to the radical form and can be expressed as v(x^3).

Let us discuss how do you divide radicals in general. Consider a radical in rational form. The division is possible if the indices of both the numerator and the denominator are same. In such a case, we can express the division of the radicands inside one symbol of the same index.

For example, v(a)/v(b) = v(a/b), b ? 0. In many cases it is possible to simplify the fraction (a/b) and at times it may turn out to a perfect power and hence the answer may be an integer free from radical sign.
Let us explain the concept of dividing radical with some examples.
v(3)/v(7) = v(3/7). In this case, the fraction cannot be simplified and this is the final answer.
v(14)/v(7) = v(14/7) . In this case, the fraction can be simplified as 2 and the final answer is v(2).
Now let us consider this one. v(28)/v(7) = v(28/7). The fraction 28/7 can be simplified as 4, which is a perfect square of 2. Therefore, in this case the answer turns out to be an integer.

There is one more concept in radical divisions. Suppose you arrive at an answer with a radical in the denominator. Never leave it in that form.
Multiply both the numerator and the denominator by the a radical which will make the denominator in integer form. This is called rationalizing the denominator.

Math Terminalogy

Introduction to math terminology:

Mathematics use a lot of terms. Mathematics term contains some symbol representation. Symbolic representation is easy to remain. Mathematics can be divided into many branches. Every branch contains many terminals to represent the mathematical word. Now we see some terms only.

Example for mathematics operation:

• Addition
• Subtraction
• Multiplication
• Division

Math Terminology in Various Branches of Maths:


Now we see mathematical terms in various branches. They are

• Math terminology in number system
• Math terminology in arithmetic
• Math terminology in measurements
• Math terminology in complex numbers
• Math terminology in geometry
• Math terminology in algebraic geometry
• Math terminology in trigonometry
• Math terminology in sets and functions
• Math terminology in analytical geometry
• Math terminology in probability

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Math Terminology:


Math terminology in number system:

The following terms are involved or used in number system. Now we see the math term with symbolic representation.

Real numbers =R
Whole number =W
Natural numbers =N
Greatest common divisor =GCD
Least common multiple=LCM
Arithmetic Progression =A.P
Geometric progression=G.P
Math terminology in arithmetic:

• Ratio
• Proportion
• Percentage
• Profit
• Loss
• Square root
• Cube root
• Time and work
• Simple interest

Ratio: Ratio means contrast of two related quantities by division.

Proportion: Proportion is a sameness of two ratios.

Percentage: A percentage is a portion whose denominator is 100.

Profit: Profit= selling price- cost price

Loss: Loss=cost price-selling price

Math terminology in measurements:

• Length
• Density
• Mass
• Breath
• Area
• Volume
• Surface area
• Curved surface area
• Perimeter

Math terminology in complex numbers:

• Real numbers
• Imaginary numbers

Math terminology in geometry:

• Circle
• Cone
• Square
• Rectangle
• Triangle
• Angle
• Line
• Trapezium
• Rhombus
• Cylinder
• Slope
• Perpendicular
• Circumcenter

Math Terminology in Probability:

• Mean
• Median
• Mode
• Standard deviation
• variance

Math Terminology in Analytical Geometry:

• Conic
• Parabola
• Ellipse
• Hyperbola
• Locus
• Circle
• Line
• Center point

Math Terminology in Sets and Functions:

• Union
• Intersection
• Associative law
• Distributive law
• Demorgor’s law
• Symmetric relation
• Transitive relation
• Equivalence relation
• Into function
• Onto function
• One to one function:
• Many to one function
• Constant function
• Identity function

Math Terminology in Trigonometry:

• Sin
• Cos
• Tan
• Cosec
• Sec
• Cot

Math Terminology in Algebraic Geometry:

• Cartesian coordinate system
• Slope of line
• Equation of straight line
• Distance between two points

Learn How to Pass Algebra

Introduction to Learn Algebra:-

Algebra is the division of arithmetic that uses letters in place of some unknown numbers. Algebra is a cluster of mathematics, which is used to create mathematical problems of valid-globe actions and control problems that we cannot explain using arithmetic. Algebra uses the cipher as calculation for addition, subtraction, multiplication and division and it includes constants, operating signs and variables. Algebraic equations represent a collection, what is finished on one side of the range with a number to the other side of the range.This kind of algebra easy to learn and easy to pass also. I like to share this Equation with no Solution with you all through my article.


Learn topics to Pass algebraWe need to study the above topics to pass:-


algebra Exponential and Logarithms

algebra Absolute Value Equations and Inequalities

algebra Sequences and Series Combinatorial

algebra Advanced Graphing

Graphing Polynomials for algebra

Graphing Rational Functions

Exponents for algebra

Radicals for algebra

Polynomials for algebra

Factoring for algebra

Division of Polynomials for algebra

Solving Equations for algebra

Solving Inequalities for algebra

We need to learn the above topics to pass algebra.


Learn tips to pass algebra:-

Distributive Law of algebra

a (b + c) = ab + ac

a (b - c) = ab – ac

Combine like variables of algebra

2a + 3a = 5a

3x + 5 + 7x = 10x + 5

9y – 4y = 5y

6c – 2 – 2c = 4c – 2

Combine like variables and exponents of algebra

4x^2+ 3x^2= 7x^2

2x^2+ 3x + 2 + 4x^2+ 3x + 4 = 6x^2+ 6x+ 6

5x^2- 3x^2= 2x^2

7x^2+ 8x + 3 - 2x^2- 4x - 2

= 5x^2+ 4x + 1

Problem:

Solve for x : X/4=-2

Solution:

X*4/4=-2*4

x = -8

Solve for x

2 x + 2 = -18

Solution:-

2x + 2 - 2 = -18 – 2

2x = -20

2x/2=-20/2

x = -10

By go through the above problems and workout the following problems, you can pass algebra.

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Practice problems for algebra:-


1. Find factors and root of the equation x^2 - 10x + 24

Answer: -6, -4

2.Find factors and root of the equation x^2 -11x + 28

Answer: -4, -7

3. Find factors and root of the equation x^2 + 2x + 8

Answer: 4, -2

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Free Algebra Answers

Introduction for learning free algebra answers:

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. The Algebra executes the four basic operations such as addition, subtraction, multiplication and division. The most important terms for learning free algebra answers are variables, constant, coefficients, exponents, terms and expressions. In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, Learning free algebra answers may be regarded as an extension of Arithmetic.

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Order of the operation for learning free algebra answers:


1. First, we have to evaluate the expressions within the parenthesis.

2. Next,  we have to evaluate the exponents.

3. Next, we have to evaluate the multiplication or division operations.

4. Finally, we have to evaluate the addition or subtraction operations.


Examples for learning free algebra answers:


Example 1:

3(a-2) + 10 = 0

Solution:

3(a-2) + 10 = 0

3a – 6 + 10 = 0

3a + 4 = 0

3a + 4 - 4= 0 – 4 (Add -4 on both sides)

3a = -4

3a / 3 = -4 / 3 (both sides divided by3)

A = -4 /3

Example 2:

5x - 10 = 15x - 20

Solution:

5x - 10 = 15x - 20

5x - 10 + 10= 15x – 20 + 10    (Add 10 on both sides)

5x =15x -10

5x – 15x =15x -15x  - 10 (Add  -15x on both sides)

-10x = -10

-10x / 10 = -10 / 10 (both sides divided by 10)

-x = - 1 which is equal to x=1

Example 3:

10x + 20 = 30

Solution

10x + 20 = 30

10x + 20 - 20 = 30 - 20 (Add -20 on both sides)

10x = 10

10x / 10 = 10 / 10 (both sides divided by 10)

x = 1

Example 4:

Solve the equation   |-25x + 50| -75 = -100

Solution:

|-25x + 50| -75 = -100

|-25x + 50| -75 + 75= -100 + 75(Add 75 on both sides)

|-25x + 50| = -25

|-25x + 50| is same as -25x + 50, now solve for x

-25x + 50= -25

-25x + 50= -25 - 50 (add -50 on both sides)

-25x=-75

-25x /- 25 = -75 / -25 (both sides divided by -25)

x = 1

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Practice problem for learning free algebra answers:


1. 4(x-6) + 15 = 1

Answer: x=2.5

2. 3x - 7 = 15x – 8

Answer: x=0.1

3. 2x + 8 = 3

Answer: x=-2.5

Learn Different Quadrilaterals

Introduction of quadrilateral:  We know that on combining three non-collinear points in pairs, the figure so obtained is a triangle. Now, let us mark four points and see what we obtain on combining them in pairs in some order. Such a figure formed by combining four points in an order is called a quadrilateral. In a quadrilateral, a pair of opposite sides is parallel. I like to share this Slope Intercept Formula with you all through my article.




Definition of Quadrilateral and its types:


Definition of Quadrilateral:   Quadrilateral is a geometrical figure that consists of f our end points called verticals joined to each other by straight-line segments or sides called edges. The quadrilateral are classified depends on the length of side, angle and diagonals of object.

Methods of Quadrilateral:

Parallelogram

Square

Rectangle

Rhombus

Trapezium

Kite

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Types of Description of quadrilateral:


Parallelogram:     Parallel lines are lines are the exactly same distance between two lines that has never cross. A couple of lines of quadrilateral that are parallelograms that you may already know about are squares and rectangles.

Formula:

Area = b × h sq. units (b – Base, h - Height)

Square:    The square is a parallelogram having an angle, equal to right angle and adjacent sides equal. Parallel lines are lines are exactly the same length and height that has never cross.

Formula:

Area = a2    (a - area)

Rectangle:     Parallel lines are the same distance between their two lines and that has never cross. Probably those angles know about a couple of lines quadrilateral that also called as parallel sides and four right angles.

Formula:

Area = l × b sq. units

Where

l – Length

and b – breadth)

Trapezoid:    A quadrilateral should have at least one pair of parallel sides. The quadrilateral one side of opposite sides are parallel if non parallel of opposite sides of a trapezoid are congruent it is called as isosceles triangle.

Formula:

Area = 1 / 2 (a + b) × h sq. units.

Rhombus:     All the four sides of this quadrilateral are equal. Rhombus is a parallelogram having its adjacent sides equal but more of whose angles is a right angles.

Formula:

Area = 1 / 2( d1 × d2) sq. units

Where

d1, d2 are diagonals.

Kite:    A quadrilateral with two pairs of equal sides and hence only one pair of equal angles. The longer one bisects its diagonal. The area of the kite is equal to the product of its diagonals.

Formula:

Area = 1 / 2 * d1 * d2

Where

d1, d2 are diagonals.