Elementary Probability

Introduction to elementary probability:

          The elementary probability started with gambling, The probability mostly used in the field of physical science, commerce, biology science, medical science, weather forecasting , etc., An experiment having more than one possible outcome is called statistical experiment. A statistical experiment is also known as a trial. Tossing a coin whether it results in a head or a tail is a trial. Certain statements implying more than one possible situation can also be termed as trials.


Elementary probability of an event

In a random experiment, let S be the sample space and E `sube` S. Then E is an event.

The elementary probability of occurrence of E is defined as

            P (E)= number of outcomes favorable to occurrence of E
                         number of all possible outcomes

                        = number of distinct element in E
                                number of distinct element in S

                        = n (E)
                           n (S)

                        Therefore P (E) = n(E)
                                                  n(S)


Elementary probability example problem

Example 1:

A coin is tossed once. Find the probability of getting a head?

Solution:

When a coin is tossed once, the sample space is given by S= {H, T},

Let E be the event of getting a head.

Then, E = {H}.

Therefore n(E)=1 and n(S)=2.

P (getting a head)= p(E)= n(E) / n(S) = 1 / 2.

Example 2:

Two coins are tossed once. Find the probability of

(i)Getting 2 heads

(ii)Getting a least 1 head

(iii)Getting no head

(iv)Getting 1 tail and 1 tail

Solution:

Where 2 coins are tossed once, the sample space is given by S= {HH, HT, TH, TT} and, therefore, n(S)=4.

(i)Getting 2 head

Let E1 = event of getting 2 heads. Then,

E1= {HH} and, therefore, n (E1) =1.

Therefore P (getting 2 heads) = P(E1) =  n(E1) / n(S) = 1 / 4

(ii)Getting at least 1 head

Let E2 = event of getting at least 1 head. Then,

E2= {HT, TH, HH} and, therefore, n (E2) =3.

Therefore P (getting at least 1 head) = P (E2) = n(E2) / n(S) = 3 / 4

(iii)Getting no head

Let E3 = event of getting no head. Then,

E3= {TT} and, therefore, n (E3) =1.

Therefore P (getting no head) = P (E3) = n(E3) / n(S) = 1 / 4

(iv)Getting 1 head and 1 tail

Let E4 = event of getting 1 head and 1 tail. Then,

E4= {HT, TH} and, therefore, n (E4) =2.

Therefore P (getting 1 head and 1 tail) = P (E4) = n(E4) / n(S) = 2 / 4 = 1 / 2.

Elementary Algebra Homework

Introduction for elementary algebra homework:

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. The elementary algebra covers that the four basic operations such as addition, subtraction, multiplication and division In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, elementary algebra  homework covers may be as they regarded as in extension of Arithmetic Understanding One-step Linear Equations is always challenging for me but thanks to all math help websites to help me out.


Basic rules and properties of elementary algebra homework:


•     Variables

Algebraic variables are the alphabetical characters which can be used for assigning the value. While solving the algebraic equation value of that variable will be changed. Widely used variables are x, y, z

•     Constant

An algebraic constants are the value whose value are never to be changed during the solving the algebraic equation. In 2y + 5, the value 5 is the constant.

•     Expressions

An algebraic Expression is the combination of that variables, constant, coefficients, exponents, terms which are combined by the following arithmetic operations Addition, subtraction, multiplication and division. The example of an algebraic expression is given below

2y + 5

•     Term

Terms of the algebraic expression is concatenated to the form of a algebraic expression by the arithmetic operations such as addition, subtraction, multiplication and division. In the following example 3n2 + 2n the terms 3n2, 2n are combined to form the algebraic expression 3n2 + 2n by the addition operation (+)

•     Coefficient

The coefficient of an algebraic expression has the value will present just before the terms. From the following example, 3n2 + 2n the coefficient of 3n2 is 3 and 2n is 2

•     Equations

An algebraic equation equals the numbers or expressions. Most probably algebraic equation is used for that an value of the variable. The example of the equation is given below

2y + 5=0

In elementary algebra, we list out the fundamental rules and properties of pre-algebra and give examples on they may be used.

Suppose that the a, b and c are variables or pre-algebraic expressions.

Suppose that the a, b and c are variables or pre-algebraic expressions.

1. Commutative Property of Addition In elementary algebra.

a + b = b + a

Examples:

1. real numbers

2 + 3 = 3 + 2

2. pre-algebra expressions

x 2 + x = x + x 2

2. Commutative Property of Multiplication In the elementary algebra.

a * b = b * a

Examples:

1. real numbers

5 * 7 = 7 * 5

2. pre-algebra expressions

(x 3 - 2) * x = x * (x 3 - 2)

3. Associative Property of Addition In elementary algebra.

(a + b) + c = a + (b + c)

Having problem with Variables and Expressions keep reading my upcoming posts, i will try to help you.


Order of the operation for elementary algebra homework


1. Reduce whatever inside the parentheses.

2. Reduce the exponents.

3. Multiplication or division.

4. Finally, perform Addition or Subtraction.

Examples of elementary algebra home work

Elementary algebra homework problem1:

5*(10+5)

Solution:

5*(10+5) = 5*10+5*5

=50+25

=75

Elementary algebra homework problem 2:

2+(4+6)

Solution:

2+(4+6)=2+10

=12

Elementary algebra homework problem 3: Find the value for the below expression if a=6

3(a-9)

Solution:

= 3(a-9) (evaluate the expression at inside the parenthesis)

= 3(6-9)

= 3(-3) which is equal to 3 * -3

= -9

Elementary algebra homework problem 4:

Simplify the following expression 4*(44÷2)

Solution:

= 4*(44÷2) (evaluate the expression inside the parenthesis)

= 4*(22)

= 88

Elementary algebra homework problem5:

Simplify the following expression 3*(27÷9)+5

Solution:

= 3*(27÷9)+5 (evaluate the expression inside the parenthesis)

= (3*3) +5

= 9+5

= 14

Math Questions and Answers

Introduction to math questions and answers:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". In this article we shall discuss about  math questions and answers.


Math questions and answers:


Some of the important math Questions and Answers are given below ,

Example 1:

Solve the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Answer:

Given the equation

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Multiply factors.

-15x - 10 - x + 3 = -16x - 20 +13

Group like terms

-16x - 7 = -16x - 7

Add 16x + 7 to both sides

0 = 0

Example 2:

Find the average marks obtained by john in his 5 test.

92, 86,90,94,96

Solution:

Number of test = 5

Marks obtained by john = 92, 86, 90, 94, 96

Average marks obtained by john in 5 test = ` (92+86+90+94+96)/5`

Average =  91.6.

Example 3:

Solve 9x2 + 6x - 3 = 0 for x.

Solution:  Factor:  (9x - 3)(x + 1) = 0

9x - 3 = 0, x + 1 = 0

9x = 3 ,      x = -1

x = (1 / 3) ,   x = -1

x = -1,(1/3)


Example 4:


Surface area of a right circular cylinder of height 30 cm is 112 cm^2. find the radius of the base.

Solution:

Curved surface area = (2?r h) = 112 cm^2

2*(22/7)* r *30 = 112

r = (7*112)/(2*22*30)

= 784/1320.

= 0.5939 cm

Hence, radius of the base = 0.5939 cm.

Example 5:

Find the median of the following set of points:

17, 16, 12, 8, 12, 9, 18, 14

Solution:

Step 1:

First arrange the given numbers in ascending or descending order.

8, 9, 12, 12, 14, 16, 17, 18

Step 2:

Here 4th and 5th number of the given observation are 12, 14

So 12 and 14 are the middle observation

Step 3:

So median of the even observation = average of the middle two numbers

Median = `(12+14)/2`

= 26/2

= 13

So the median is 13.

Elementary Math Geometry

Introduction to elementary math geometry :

Geometry plays their important part in the mathematics in which it deals with the shapes like cone, circle, square, rectangle and their positions in the spaces and the measurement of the shapes using parameters like area, volume and perimeter.  Elementary geometry problems includes solving simple basic level math problems. Here we will solve some elementary math problems. In this article we will brief about elementary math geometry. I like to share this Equation Parabola with you all through my article.
 
Elementary Math Geometry:

Elementary math geometry involves in preparing geometry math problems. Here we will see some sample problems as below,
Example problem 1- Elementary math geometry

What is the area of the square whose sides measures 7cm?

Solution:

Area of the square = side 2

= 7 2

= 49

Area of the square = 49 cm 2

Example problem 2:

Find out the diagonal of the rectangle whose length is l =15 cm and breadth is b = 6 cm?

Solution:

Diagonal of the rectangle  = `sqrt(l^(2) + b^(2))`

= `sqrt(15^(2) + 6^(2))`

= `sqrt(225+ 36)`

= `sqrt(261)`

= 16.15

Diagonal of the rectangle = 16.15 cm

Example problem 3:

What is the area of the trapezoid whose side measures a = 9 cm and b = 7 cm and height measures h =6 cm?

Solution:

In the trapezoid, consists of  4 sides; out of the four sides 2 sides are parallel.

Area of the trapezoid = `1 / 2` (a + b) * h

= `1 / 2` (9 + 7) * 6

= `1 / 2(` (16) * 6

= 8 * 6

Area of the trapezoid = 48 cm2

Example problem 5:

The angle of a triangle is 120. Then what is the measure of its supplementary angle?

Solution:

Supplementary angle is 180.

Given angle of the triangle is 120.

Supplementary angle to measure for 120= 180 – 120

= 60


Understanding Math Help Geometry is always challenging for me but thanks to all math help websites to help me out.

Practice Problem: Elementary Math Geometry

Practice problem 1 - Elementary math geometry
What is the area of the square whose sides measures 8cm?

Answer: 64cm 2

Practice problem 2 - Elementary math geometry

The angle of a triangle is 160. Then what is the measure of its supplementary angle?

Answer: 20

Two Hundred Forty

Introduction to two hundred forty:

In this article we shall discuss the finding two hundred forty. The below given are the various place values. The number two hundred forty (240) is a natural number. In this article we shall discuss about factors solving problems related to two hundred forty (240). It is three (3) digits number with,

0 is once place,

4 is tens place,

2 is hundreds places,

The numbers

Two hundred forty numbers is between 239 and 241. Please express your views of this topic Math Median by commenting on blog

Factors of Numbers Two Hundred Forty:

The factors two hundred forty:

The factors two hundred forty are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.

The numbers two hundred forty factor pairs are:

1 x 240,

2 x 120,

3 x 80,

4 x 60,

5 x 48,

6 x 40,

8 x 30,

10 x 24,

12 x 20,

15 x 16,

20 x 12,

24 x 10

30 x 8,

40 x 6,

48 x 5,

60 x 4,

80 x 3,

120 x 2,

and 240 x 1.

Is this topic List Odd Numbers hard for you? Watch out for my coming posts.

Example Problems for Two Hundred Forty:

Example 1:

Add 200 to two hundred forty.

Solution:

The given things are 200 + 240.

By adding this two we get 200+ 240.

440.

So the sum of 240 and 200 is 440.

Example 2:

Find the value of 2402?

Solution:

We need to find the value of 2402.

2402 = 240 x 240.

The product of 240 x 240 is 57600

Example 3:

Find the value of 240 +240 =?

Solution:

We need to find the value of 240 + 240.

The product of 240 + 240 is 480.

Example 4:

Find the value of 240 + 240 + 240 =?

Solution:

We need to find the value of 240 + 240 + 240.

240 + 240 + 240= 720

The product of 240 + 240 + 240 is 720.

Example 5:

Find the reciprocal of the number 240

Solution:

The given element is 240 we need to find the reciprocal of the element.

The basic syntax that finds the reciprocal of the element y is ` 1/y`

Here the number is 240.

By plugging in the given values in to the formula we get

240= `1/240`

So the reciprocal of the number 240 is `1/240`

Example 6:

Find the reciprocal of the number `50/240`

Solution:

The given number is `50/240` we need to find the reciprocal of the number.

The basic syntax that finds the reciprocal of the element` x/y`  is `y/x.`

Here the number is `50/240` .

By plugging in the given values in to the formula we get

`50/240` =`240/50`

So the reciprocal of the number `50/240` is `240/50` .

The simplify reciprocal solution is 4.8

The Math Term for Conjecture

Introduction to math term conjecture:

The term conjecture in math refers a statement or assumptions that are not proved. It is like a theorem, but they have not proved. For example the kite area conjecture states that the area of kite is equal to half the product lengths of two diagonals. The term Conjecture can be also mean as rules or conditions. In this article we shall some math conjectures and example problems.

Math Term for Conjecture – Formulas:

Rectangle area conjecture:

Area of rectangle (A) = b x h square units

Where,

A – Area of rectangle

b – Length of the base

h – Height of the rectangle

Trapezoid area conjecture:

The diagram of trapezoid is shown in below.

Area of trapezoid (A) = `1/2` x h x (a + b) square units

Where,

A – Area of trapezoid

h – Height

a, b – length of two parallel sides

Circle area conjecture:

The diagram of circle is shown in below

Area of the circle (A) = pr2 square units

Where,

A – Area of circle

r – Radius of circle

Having problem with Cube Root Formula keep reading my upcoming posts, i will try to help you.

Math Term for Conjecture – Example Problems:

1. The rectangle has base length 10.5 cm and height 5.5 cm. solve for area of rectangle.

Solution:

Given:

Base Length (b) = 10.5 cm,

Height (h) = 5.5 cm

Solving area:

Rectangle area conjecture:

Area of rectangle = b x h square unit.

= 10.5 x 5.5

Area of rectangle = 57.75 cm^2

2.      Find the area of trapezoid whose height 13.5 cm, side a= 7.5 cm and side b= 9.5 cm

Solution:

Given:

Height (h) = 13.5 cm

Side a= 7.5 cm;            b= 9.5 cm

Formula:

Area of trapezoid (A) = `1/2` x h x (a + b) square units

=`1/2` x 13.5 x (7.5 + 9.5)

=`1/2` x 13.5 x 17

=`1/2` x 229.5

= `229.5 / 2`

= 114.75

Area of trapezoid (A) = 114.75 cm^2

3. The radius of a circle is 8.5 cm. Find the area of that circle?

Solution:

Given:

r = 8.5 cm

Formula:

Area of the circle = p x r^2

p = 3.14

A = 3.14 x (8.5)^2

=3.14 x 72.25

Area of circle = 226.86 cm^2

Definition of Exercise in Math

Introduction for Math Exercise:

Collection of practice problem is known as exercise. If a student wants some definition in math exercise with problems, they can refer to the below examples. In this we can see some of the math exercise in statistics with example problems as shown. Let us see some of the general math exercise in statistics such as mean, median and mode with examples and practice problems as follows.

Definition of Exercise in Math – Definitions for Exercise:

In this following we can see some math definition for statistics exercise.

Mean:

It is a set of data which can find the average in dividing by sum of numbers with total numbers in the given data.

Median:

It is a set of numbers which can find the middle numbers and arrange the numbers in order to select the middle number.

Mode:

It is a set of numbers that can occur frequently in a set of data and no number can occur more than once.

Definition of Exercise in Math – Examples and Practice Problems:

In this following we can see some math definition for statistics exercise with example and practice problems.

Math Definition for Exercise 1:

Find the mean of weights for 6 peoples in kilograms are 4, 1, 9, 2, 11, and 3.

Solution:

Sum of numbers
Mean = ------------------------------
Total number

= `(4+1+9+2+11+3)/6`

= `30/6`

= 5

Math Definition for Exercise 2:

Find the median of 16, 1, 15, 13, 20, and 8.

Solution:

Arrange the data in ascending order as 1, 8, 13, 15, 16 and 20.

N = 6

Since n is even, median = `1 / 2` [`(nth)/2` item value + (`n / 2` + 1)th item value]

= `1 / 2` [6th item value + (`6/2` + 1)th item value]

= `1 / 2` [3rd item value + 4th item value]

= `1 / 2` [13 + 15]

= `1 / 2` * 28

= 14

Math Definition for Exercise 3:

Find the mode of 23, 19, 28, 13, and 28.

Solution:

28 are repeated twice.

Mode = 28

Practice Problems:

Find the mean of weights for 6 peoples in kilograms are 8, 1, 10, 2, 7, and 3.

Solution:

= 5.16

Find the median of 19, 14, 6, 8, 3, and 12.

Solution:

= 10

Find the mode of 17, 19, 16, 24, and 19.

Solution:

= 19