Definition of Probability

Introduction to Probability Definition:

In math, the probability is one of the important and very simple subjects. Generally the probability is defined as something will be happening. The probability contains sample space, events and experiments. The probability has many types; the two important types are Poisson distribution probability and binomial distribution. Now we will see the definition of probability. I like to share this Law of Probability with you all through my article.

Definition of probability:

Definition of  probability is a possible outcome of a particular process.The part of math that studies the possibility of incidence of random events in order to predict the actions of defined systems.The Probability is a method of expressing knowledge that an action will happen or has occurred.

Formula for Probability:

Probability =` ("Number of probable events")/ ("Total given events")` .

Now we will solve the some of example problems with help of probability formula. Understanding Y=mx+b Calculator is always challenging for me but thanks to all math help websites to help me out.


Example 1:


In a class room 48 students are studying some subjects. In that class room 16 students are studying math subject, 12 students are studying physics subject and 20 students are studying biology subject.What is the probability for,

i. Select the Math students.

ii. Select the biology students.

Solution:

Step 1:

Given:

Total students n(S) = 48.

Studying math students n (A) =16.

Studying Physics students n (B) = 12.

Studying Biology students n(C) = 20.

Step 2:

i. Probability for getting math students:

P (event) = `("Number of favorable math students")/("Total students").`

Number of math students = 16.

Total students = 48.

= `16/48` .

=` 8/24` .

ii. Probability for selecting biology students:

Step 1:

P (event) = `("Number of favorable biology students")/("Total students").`

Here number of biology students = 20.

Total students = 48.

= `20/48`

=`5/12`


Example 2:


The three coins are flip at the same time. What is the probability of getting exacting two tails or three heads?

Solution:

The sample space, when three coins tossed is,

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

A be the event of exacting two tails,

n (A) = {HTT,THT,TTH,TTT} = 4

B be the event of getting exacting three heads,

n (B) = {HHH} = 1

P (A) =`4/8`

P (B) = `1/8`

P (A or B) = P (A) + P (B)

= `4/8` + `1/8` .

=` 5/8` .

= 0.63

The expected value in this probability model is 0.63.

The above information is the definition of probability.

3rd Grade Learning

Introduction for 3rd grade learning:
Third Grade Mathematics is the science of pattern and relationships. It is the language and logic of our scientific world. Mathematical power is the capability to explore, to imagine, to reason logically and to use a diversity of mathematical methods to solve problems - all important utensils for children’s futures. A mathematically great person should be able to:

Reason mathematically.
Communicate mathematically.
Solve problems using mathematics.
Make connections in mathematics and between mathematics and other field. I like to share this Integral Table Exponential with you all through my article.

3rd grade topics:


Where to Look From

Fun with numbers

Give and take

Long and short

Shapes and Designs

Fun with give and take

Time goes on

Who is heavier?

How many times

Play with patterns

Jugs and mugs

Can we share?

Smart charts

Dollars and cents.

Understanding Properties of Limits is always challenging for me but thanks to all math help websites to help me out.

Explanation for 3rd grade learning:


Where to look from?

Viewing of things varies from person to person. This lesson contains about how to look the object.

Fun with numbers:

To have more practice of numbers we have funs like,

Identify number of dots in each circle, Fill in the blanks, counting…

Give and take:

The question will be given and we have to find the answer in fun manner.

Long and short:

There is something given with the diagram. We have to give the answer according to the distance and pattern.

Shapes and design:

Some of the shapes will be given then we have to do some design with the given shapes.

Fun with give and take

Real type of questions will be given then we have to find the answer.

Time goes on

In this we have funny stories with questions that question related to minutes, hours, seconds, number of times, year etc.,

Who is heavier?

In this different type of quantity will be given then we have to find which quantity is heavier.

How many times?

This contains about multiplication with funny pictures.

Play with patterns

We have to find the pattern for the given figures.

Jugs and mugs

Stories of drink related will be given then we have to find the answer with the help of the given story.

Can we share?

This topic contains about the division problem with funny ways.

Smart charts

This contains some real pattern with that we have to find the answer.

Dollar and cents

This topic contains the problem related to Dollar and cents.

Algebra Velocity

Introduction:

Algebra  was popularized in near the beginning ninth century by al-Khowarizmi. The author of the first algebra book was preferred by , Al-jabr wa'l Muqabalah, from which the English word algebra is derived. It remained the standard text in algebra for a long time. The title translates almost to "restoring and balancing, " referring to the primary algebraic method of performing an operation on one side of an equation and restoring the balance, or equality, by doing the same thing to the other side.


Definition:

Velocity  can defined as vector measurement of the rate and direction of movement or, in other terms, the rate and direction of the change in the position of an object. The scalar  magnitude value  of the velocity vector is the speed of the motion. In mathematical terms, velocity is the first derivative of position with respect to time.

More about velocity:

1)  Velocity is a vector quantity.

2)  It is also defined as the distance per unit time, i.e.,  if  s  is distance traveled in time t, then velocity

3)  m/sec,cm/sec,ft/sec,km/hr,miles/hr etc.

4)  Velocity V =  ds / dt

.             Here,

s – Position vector

ds – First derivative of Position vector

t –  time

Please express your views of this topic Formula for Percent by commenting on blog.

Examples:

1. Find the velocity of Ed . it covers a distance of 225 miles in 5 hrs..

velocity   V  = 225 / 5   miles/sec.

velocity   V =45 miles/sec.

2. A submarine descends -120 ft in 6 seconds. What is the velocity of the submarine?
Choices:
A. 30 ft per second
B. - 30 ft per second
C. - 20 ft per second
D. 20 ft per second
Correct Answer = C
Solution:

Step 1:  Velocity = Displacement nt / time .

Step 2:  Since  submarine is descending, the displacement will be negative.

Step 3:  Displacement =120 ft and Time = 6 sec

Step 4:  velocity = -120 / 6 [Substitute the values of displacement and time.]

Step 5:  velocity = 20 [Divide.]

Step 6:  So, The velocity  = - 20 ft / second.


Velocity terms:

Displacement
Distance
Position
Rate
Rate of Change
Speed
Time
These are the various terms involved in velocity.

5th Grade Math Test

Introduction to 5th grade math test:

The given below questions are taken from 5th grade math standard test. All questions on the educational standards test are evaluated by committees.
The committees of educational standards contain content experts, test board, teachers and administrators.
The committee gives some suggestions and advice to teachers for leading the 5th grade students.
Through the test teachers improve the qualities like memory, understand, and remember characteristics of 5th grade students.
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. In this article we shall discuss algebra math help. Understanding Math Answers Free is always challenging for me but thanks to all math help websites to help me out.


Example for 5th Grade Math Test


Some of the examples for the 5th grade math test are as follows:

Example 1: This problem demonstrates the proper use of the distributive property.

Solve 4(x + 2 + 9) = 56.

Solution:

Combination of the terms like below, the left side of the equation becomes

4× (x + 2 + 9) ==> 4× (x + 11)

In here we are using the distributive property,

4 × (x + 11) ==> 4 × x + 4 × 11

Carrying out multiplications,

4 × x + 4 × 11 ==> to 4x + 44

The equation now becomes

4 x + 44 = 56.

Subtracting a 44 (adding a -44) to each side gives us

4x + 44 + (-44) = 56 + (-44)

4x + (44 + (-44)) = 56 - 44

4x + 0 = 12

4x = 12

Since the x is multiplied by 4, we divide the value on both sides by 4 to solve for x:

4x = 12

4x ÷ 4 = 12 ÷ 4

(4x)/4 = 3

x = 3.

We get the answer value is X = 3

We can test this solution of the given equation:

4 × (3 + 2 + 9) = 56

4 × 14 = 56

56 = 56 so our answer is correct.

Example 2: Evaluate the following math sum 3(x^2 + 4x) - 3y given that x = 2 and y = -5

Solution:

Given:

x=2

y=-5

3(x^2 + 4x) - 3y   We put 2 in the expression anywhere x appears, and we put -5 in the expression anywhere y appears, and the result is:

3(22 + (4) 2) - 3(-5)

Simplify it (parentheses first), we get:

3(4 + 8) - 3(-5) = 3(12) - 3(-5)

Now after the multiplication step, we get

36    - (-15)

Now, we need to do subtraction, we get

36 + 15

Finally, doing the addition, we get 51

Please express your views of this topic 6th grade math formulas by commenting on blog.


More Example:


Example: Solve x^2 + 5x + 6 = 0 and give the smallest integer of x as final value.

Solution:

x^2 + 5x + 6 = 0

x^2 + 2x + 3x + 6 = 0 (since +6 and +5 is the product and addition value of +2 and +3)

x (x + 2) + 3 (x + 2) = 0

(x + 2) (x + 3) = 0 (taking (x + 2) value as common)

x + 2 = 0, x + 3 = 0

Therefore the value of x = -2 and x = -3.

Exercise: Evaluate the following math sum 3(2x + 5) - 2y given that x = -2 and y = 4. (Answer: -5)

Statistics Help Online

Introduction to statistics help online:

The process of Collection of data with a specific purpose and to answer the question is called Statistics.

Or

Statistics is the process of drawing facts from numerical data. Statistics includes the collection of the data, presentation of the data and interpretation of the data. I like to share this Sample Size in Statistics with you all through my article.


Facts and Definition of statistics help online


Array: Raw data does not provide any useful information but it creates confusion. The data in the above form is called ' Ungrouped data ' . An Array is an arrangement of raw numerical data in the ascending or descending order of magnitude.

Range: The difference between the maximum and the minimum observations is called Range. Please express your views of this topic Decimal Definition by commenting on blog.


Statistical data and collection:
The fact collected for the purpose of investigation is called Statistical data.
There are two types of data:
Primary data
Secondary data

Primary data: The data collected by the investigator for the first time for his own use.
Secondary data: The data collected by a secondary source other than the investigator e.g.
Raw data: The data obtained from the original source but not arranged properly is called “Raw data”

Presentation of Data statistics help online

Presentation of Data: To convert a raw or an ungrounded data into grouped data.

Step 1: Determination of the range.

Step 2 : Fixation of Class Interval: There is not hard and fast rule of determining the number of classes. It is advisable to have total number or classes between 5 and 15.

Step 3: Fixation of Class Size: Divide the range by desired number of classes to determine the approximate size of the class interval.

Step 4 : To find class limits:

Classes should not be overlapping.
There should be no gaps between the classes,
Classes should be of uniform (or same) size.
Open ended classes, for example less than 5 or more than 10 etc. should not be used.

We take each observation from the data one at a time and place a tally mark “ l “ opposite the class to which the item belongs by cutting the numbers from the data.

The counting of tally marks in a particular class tells the frequency of that class. The sum of all the frequencies should be equal to the number of observations.

Kite Geometry

Introduction to  kite geometry:

Geometry is a study of size, shape and properties of objects or figures. English word ‘Geometry’ is derived from the Greek word ‘Geo’ meaning ‘earth’ and ‘metron’ means ‘Measuring’. Euclid who lived in 300 B.C. was distinguished Greek mathematician known as the ‘Father of geometry’

‘Quadrilateral’ is four sides geometric figure which has 4 edges and four angles. Kite is one of the quadrilaterals. Here we are going to see about kite geometry.


Properties of geometry kites:


1. Diagonals:

The diagonals of kite which bisects each other at right angles to form 90 degrees.

2. Area of kite:

The areas of a kite which can be calculated by the following methods .They are

1. The method of using diagonals measurement

Area = (d1*d2)/2

2. The method of using trigonometry

Area = ab sin c

3. Perimeter of kite:

The measurement of each of its sides gives the perimeter of kites.

4. A kite can become a rhombus:

A kite consists of four sides having its adjacent length are same and it looks like rhombus

The adjacent sides of kites are equal in its measurement. The opposite angles are not equal when its length are equal .I have recently faced lot of problem while learning Find the Perimeter of a Polygon, But thank to online resources of math which helped me to learn myself easily on net.


Problems for kite geometry:


Example 1:

The two diagonals of kites are d1 = 12 cm and d2 = 16 cm .Find the area of the kite?

Solution:

The area of kite which can be given as follows,

Area = (d1×d2)/2

= (12 × 16)/2

= 192/2

= 96 cm^2

Example 2.

Find the perimeter of the kite whose sides are 3,3,6,6.

Solution:

The perimeter of the kite can be given as the sum of all the sides.

Perimeter = 2a + 2b

= (2 × 3) + (2 × 6)

= 6 + 12

= 18 cm^2

Example 3:

Find the area of the kite where its sides and angle are 30 and a = 12 cm and b = 15 cm

Solution:

Area = ab sin c

= (12 × 15) sin 30

= 180 sin 30

= 180 × (1/2)

= 90 cm^2

Applied Probability

Introduction of applied probability:

Analysis of random situation, condition, or events is called Probability. Probability is the numerical analysis of impossibility to absolute certainty. Probability is the possibility that something will happen - how likely it is that some event will happen. For example, when picking a one card of diamond from the pack of 52 cards, the probability of picking a diamond card is 13/52, or 1/4.


Formulas for applied probability


Formula 1: Compliment

If AA and A'A' are complements then P(A) + P(A' ) = 1P(A)+P(A' )=1

Formula 2: Addition Rule

P(A OR B) = P(A) + P(B) - P(A AND B)P(A OR B)=P(A)+P(B)-P(A AND B)

Formula 3: Mutually Exclusive

If AA and BB are mutually exclusive then

P(A AND B) = 0P(A AND B)=0 ; so

P(A OR B) = P(A) + P(B)P(A OR B)=P(A)+P(B).

Formula 4: Multiplication Rule

P(A AND B) = P(B) P(A|B)P(A AND B)=P(B)P(A|B)

P(A AND B) = P(A) P(B|A)P(A AND B)=P(A)P(B|A)

Formula 5: Independence

If AA and BB are independent then:

P(A|B) = P(A)P(A|B)=P(A)

P(B|A)= P(B)P(B|A) =P(B)

P(A AND B) = P(A) P(B)

Understanding Partial Fraction Method is always challenging for me but thanks to all math help websites to help me out.

Examples for applied probability:


Applied Probability Problem 1: A die is rolled, find the probability that an odd number is obtained.

Solution:

Let us first write the sample space S.

S = {1,2,3,4,5,6}
Let E be the event "an odd number is obtained" and write it down.

E = {1,3,5}
We now use the formula of the classical probability.

P(E) = n(E) / n(S) = 3 / 6 = 1 / 2
Applied Probability Problem 2: Two coins are tossed, find the probability that two tails are obtained.

Solution 2:

The sample space S is given by.

S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two tails are obtained".

E = {(T,T)}
We use the formula of the classical probability.

P(E) = n(E) / n(S) = 1 / 4