How to do Probability Math

Probability Math

In mathematics, probability means likelihood of the outcome of an event of a particular experiment. The probability of event E is written P(E). Probabilities are occurs always numbers between 0 and 1. The set of all possible outcomes of a particular experiment is referred to as sample space. For example, the probability of getting a tail when tossing a coin is 1/2. Please express your views of this topic Continuous Random Variable by commenting on blog.


Probability Math - Example Problems


Example 1:

25 tokens numbered from 1 to 25, two tokens are drawn simultaneously. Find the probability that:

a) Both the tokens drawn have prime number

b) None of the tokens drawn have a prime number

Solution:

We want to select 2 tokens from 25 tokens.

n(S) = 25C2 = 25! / (2! x 23!)

= (25 x 24) / 2

= 300

a) Let A = Event that both the tokens have prime numbers.

Prime numbers between 1 to 25 are: 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Total Numbers = 9.

We have to select 2 numbers from these 9 numbers.

n(A) = 9C2 = 9! / (2! x 7!)

= (9 x 8) / 2

= 36

P(A) = `(n(A)) / (n(S)) `

=` 36/300 `

= `3/25`

b) Non prime numbers between 1 to 25: 25 - 9 = 16

Let B = Event that both the tokens have non-prime numbers.

Now we have to select 2 numbers, from 16 numbers.

n(B) = 16C2 = 16! / (2! x 14!)

= (16 x 15) / 2

= 120

P(B) = n(B) / n(S)

= 120 / 300

= 2/5

Example 2:

A bag contains 5 mangoes and 5 oranges. Two fruits are taken at random. Find the probability that both will be of the same kind.

Solution:

Let S = Sample space

A = the event of taking 2 mangoes.

B = the event of taking 2 oranges.

(A or B) = The event of taking 2 mangoes or 2 oranges.

i.e. the event of taking 2 fruits of same kind.

n(S) = 10C2 = 10! / (2! x 8!) = 10 x 9 / 2= 45

n(A) = 5C2 = 5! / (2! x 3!)

= 5 x 4 / 2

= 10

n(B) = 5C2 = 5! / (2! x 3!)

= 5 x 4 / 2

= 10

P(A) = n(A) / n(S)

= `10/45`

= `2/9`

P(B) = n(B) / n(S)

= `10/45`

= `2/9`

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

=`2/9+2/9`

= `4 / 9`

P(A or B)  = 4/9

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Probability Math - Practice Problems


Problem 1:

10 tokens numbered from 11 to 20, two tokens are drawn simultaneously. Find the probability that both the tokens drawn have prime number

Answer: 2/15

Problem 2:

2 dice are thrown simultaneously. What is the probability of getting an odd number as the sum?

Answer: 1/2

Basic Laws of Math

Introduction to basic laws of math:
Mathematics contains the some basic laws. The basic laws are used to calculate the mathematical problems easily. Following are the basic laws of arithmetic: Addition, Subtraction, Multiplication, and Division. The addition is identifying as the grouping of numbers. ‘+’ sign used for represent the addition. The subtraction is identifying as the difference of numbers. ‘-’ sign used for represent the subtraction. The multiplication is identifying as the product of numbers. ‘× ’ sign used for represent the multiplication. The division is identifying as the opposite method of multiplication. ‘/’ sign used for represent the multiplication. Mathematics has the other important law is exponent. The exponent of a number defined as how many times to we can utilize the number in a multiplication. For example: 43 = 4 × 4 × 4= 64.

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Basic laws of math:


Basic laws in math:

Addition

Subtraction

Multiplication

Division

Exponent

Basic laws of addition:

Commutative law:

Let us consider the two variables a and b we can written the commutative law of addition in the following way

a + b = b + a

Associative law:

Let us consider the three variables a, b and c we can written the associative law of addition in the following way

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

Basic laws of multiplication:

Commutative law:

Let us consider the two variables a and b we can written the commutative law of multiplication in the following way

a × b = b × a

Associative law:

Let us consider the three variables a, b and c we can written the associative law of multiplication in the following way

a(bc) = (ab)c

Distributive law:

Let us consider the three variables a, b and c we can written the distributive law of multiplication in the following way

a(b + c) = ab + ac

Subtraction:

Subtraction is the inverse method of addition.

Example:

10 - 2 = 8

Division:

Division is the inverse method of multiplication.

Example:

`12/6 = 2`

Laws of Exponents:

Assume two variables a and b

a0=1

a1= a

a-1=`1/a`

` (a^(x))/(a^y)` =ax-y

ax ay=ax+y

(ax)y = ax y

(ab)x= ax bx


Examples for basic laws of math


Example 1:

Solve: 14 + 8 = ? + 14

Solution:

Given: 14 + 8 = ? + 14

By the commutative law of addition,

a + b = b + a

14 + 8 = ? + 14

The missing value is 8

Example 2

Solve: 4 (5 + x) = 40

Solution:

Given: 4 (5 + x) = 40

By the distributive law of multiplication,

4 (5 + x) = 40

4 (5) + 4(x) = 40

20 + 4x = 40

4x = 40 - 20

4x = 20

x = `20/4`

x = 5

Example 3

Prove: 4 +(6 + 7) = (4 + 6) + 7

Solution:

Given: 4 +(6 + 7) = (4 + 6) + 7

4 + (13) = (10) + 7

17 = 17

Therefore, the given statement is true. Understanding Partial Derivative Calculator is always challenging for me but thanks to all math help websites to help me out.


Practice problems for basic laws of math:


Problem 1:

Find the value of x: 6 (4 + x) = 48

Answer: x = 4

Problem 2:

Prove: 10 +( 5 + 8) = (10 + 5) + 8

Anti X Math

Introduction to anti x math:

In this article we are going to see anti x math. We know that math is large volume that used to resolve and discover so many things in the world. In math, variable is an most important part that used to get a input values. Most commonly we use x as a variable for most of the problems. Here we are going to see how to find anti(inverse) x of the variable x.

Anti x can be called as inverse of x or reciprocal of x . The reciprocal of the variable x can be find by interchanging the numerator and its denominator. The inverse of the function can be find by solving for x from y. Every function has its inverse. But not  every inverse function has function


Problems on anti x math:


Problem 1:

The variable `x = 12 / 5` . Find the value of anti x.

Solution:

Given , x = `12 / 5`

We need to find the anti x.

In this problem anti x mean that the multiplicative inverse or reciprocal.

To find the reciprocal, change the numerator into denominator and vice verse.

`x = 12/5`

Taking reciprocal on both sides,

`1/x = 5/12`

We can write `1/x = x^(-1)`

`x^(-1) = 5/12`

Answer: `x^(-1) = 5/12`

Problem 2:

Find the inverse of the function y = 5x - 8

Solution:

Given, y = 5x - 8

We need to find the the inverse of the given function.

To find the inverse of the function we need to solve for x.

y = 5x - 8

Add 8 on both sides,

y + 8 = 5x - 8 + 8

y + 8 = 5x

Divide by 5 on both sides,

`( y + 8 ) / 5` = 5x / 5

`( y + 8 ) / 5` = x

x = `( y + 8 ) / 5 `

Answer: x = `( y + 8 ) / 5 `

Understanding Truth Table Generator is always challenging for me but thanks to all math help websites to help me out.

Practice problems on anti x math :


Problems:

1. Find the anti x of  x = 54 / 67

2. Find the inverse of the function f(x) = 9x - 6

Answers:

1. `x^(-1) = 67/54`

2. `f^(-1)(x) = (x+6) / 9`

Math For All Seasons

Introduction of math for all seasons:

The math for all seasons is nothing but the ways for solving the problem solving to children. It helps you to get the idea how to find the solution for the particular problem. The children can develop their ideas on grouping for the arithmetic operations like addition and subtraction. Also we give the idea to find the way to save the time on the particular problem. Please express your views of this topic Solving Equations Using Addition and Subtraction by commenting on blog.


Math for all seasons:


The children can have the idea to solve the pattern and symmetric problems. These topics give the various types of problems which makes you excel in each topic. Hence the math for all seasons gives you ideas for solving all the subtopics in math.


Example for math for all seasons:


Example 1: Compute the math partial sums of (355 +565).

3 6 6

4 8 5

Add 100s                  7 0 0

Add 10s                     1 4 0

Add 1s                       1 1

Add partial sums    8 5 1

Step 1: first sum up the place value of hundred = 700.

Step 2: Then sum up the ten place values = 140.

Step 3: Then sum up the one place values = 11.

Step 4: Finally sum up all the partial values to compute the solution = 851.

Is this topic Associative Property of Multiplication Example hard for you? Watch out for my coming posts.

Example 2: Compute the math partial sums of (243 + 134).

2 4 3

1 3 4

Add 100s                3 0 0

Add 10s                   7 0 0

Add 1s                     7 0 0

Add partial sums 3 7 7

Step 1: First sum up the place value of hundred = 300.

Step 2: Then sum up the place value of tens = 700.

Step 3: Then sum up the place value of ones = 700.

Step 4: Then sum up all the partial values to compute the solution = 377.

Example: What is +4+ (+2)?

From above: + (+) becomes a positive sign.

+4+ (+2) = +4 + 2

Start at +4 on the number line, move forward 2, and you end up at 6

Answer: 4+ (+2) = 6

Example: Find out the place value and the face value of the each digit in the number 78,234,543.

Solution:         Face value (digit)                                Place value (digit)

7                                                            70,000,000

8                                                                8,000,000

2                                                                   500,000

3                                                                      30,000

4                                                                         4000

5                                                                           500

4                                                                             40

3                                                                              3

The above sequence of number can be written as “seven eighty million two hundred and thirty four thousand and five hundred and forty three”.

Math Partial Sums

Introduction of math partial sums:

The math partial sums deal with the numerical values and their operations on math. This system involves natural numbers, integers. The arithmetic operations which deals with positive numbers and negative numbers. The natural numbers which includes all the whole numbers. The natural numbers sets are denoted as N. The number systems have the ability to count. The collections of some features are termed with number systems.


Math partial sums:


The math partial sums includes the two stages in which the first stage looks at the columns present, works from left to right and we should sum up the place values of the digits present in the particular column. The negative number systems are the one which is lesser than the zero.

The negative numbers are followed by the sign (-). The negative number systems are also denoted as the inverse of the number. The positive number systems are which are larger than zero. It is the most used number systems found in our day to day life. The second stage of the math partial sums includes the place values sum up together. Please express your views of this topic An Odd Number by commenting on blog.


Examples for the math partial sums:


Ex 1: Compute the math partial sums of (355 +565).

3 6 6

4 8 5

Add 100s                  7 0 0

Add 10s                     1 4 0

Add 1s                       1 1

Add partial sums    8 5 1

Step 1: first sum up the place value of hundred = 700.

Step 2: Then sum up the ten place values = 140.

Step 3: Then sum up the one place values = 11.

Step 4: Finally sum up all the partial values to compute the solution = 851.



Ex 2: Compute the math partial sums of (243 + 134).

2 4 3

1 3 4

Add 100s                3 0 0

Add 10s                   7 0 0

Add 1s                     7 0 0

Add partial sums 3 7 7

Step 1: First sum up the place value of hundred = 300.

Step 2: Then sum up the place value of tens = 700.

Step 3: Then sum up the place value of ones = 700.

Step 4: Then sum up all the partial values to compute the solution = 377.

Learn Math Facts Fast

Introduction to learn math facts fast:
A fact is a group of a declaration of each of which stand for the same meaning. All the declaration has the same meanings. Addition and subtraction facts contain 2 or 3 numbers. The types of facts operations are addition and subtraction facts, multiplication and division facts. In here we shall discuss about learn math facts fast. Having problem with Decimal to Percent Calculator keep reading my upcoming posts, i will try to help you.

Addends:

The facts being added in an addition operation like 7 and 4 in 7 + 4 = 11 or 4 + 7 = 11.

Reverse operation:

Reverse of a process is call as inverse operation of addition and subtraction.


Sample problem for math facts fast learn:


First we take an addition operation like 3 + 5 = 8.

In the next operation the addends are reversed like 5 + 3 = 8.

Now we can write the inverse operations of the above values both.

8 - 5 = 3

8 - 3 = 5

Addition and subtraction math facts fast learn:

Example 1:

What are the members of the fact family of 11 + 9 = 20?

Solution:

11 + 9 = 20

Reversing the addends:

9 + 11 = 20;

Inverse operations:

20 - 9 = 11;

20 - 11 = 9;

When we are modify the order to addition, then answer will be based on the numbers which we in use to do the addition process.

Example 2:

Write the facts of the family with numbers 9, 5 and 14.

Solution:

9 + 5 = 14;

5 + 9 = 14;

14 - 9 = 5;

14 - 5 = 9;

When 2 of the numbers are same, then we have only 2 facts. Because, the 1st two and last two fact values are same. Please express your views of this topic Cone Volume Formula by commenting on blog.


Division and multiplication math facts fast learn :


Example 1:

Write the facts of the family with numbers 11, 5 and 16.

Solution:

In the problem we find the facts value for division and multiplication.

11 * 5 = 55

5 * 11 = 55

55 / 11 = 5

55 / 5 = 11

When 2 of the numbers are same, then we have only 2 facts. Because, the 1st two and last two fact values are same

Example 2:

Write the four facts of the family with numbers 2, 7 and 9.

Solution:

7 * 2 = 14

2 * 7 = 14

14 / 2 = 7

14 / 7 = 2

When 2 of the numbers are same, then we have only 2 facts. Because, the 1st two and last two fact values are same

Equations With No Solution

Equations with no Solution

Intoducion:

There are two types of equation.one is equation with solution and other is equation without solution.in equation with solution we can find the value of variable like x,y,z.but in the equation with no solution we can  not find the value of variable like x,y,z.in the equation with no solution we can get situation like 0=0,4=5,7=8 etc...For equations with solutuion,we can solve the equation by three method.these methods are 1)Elimination method 2)Substitution method 3)Graphing method..by these method we can check that whether a equation has solution or not?

When we solve by Elimination method we have to make the coefficient of one the variable into equal and then add both the equations. Now one of the variables will get cancel and then one of the variables is left out. After that, solve for the left variable. Finally substitute the result of one of the variable in any one of the equation we will get the result for another variable. When we solve by substitution method substitute one of the equation in another and then solve. If we are solving by graphing method draw a graph for both the equation in a single graph. The intersection point of the lines is a solution for the given system of linear equation. So these are method of solving a linear equation.


DESCRIPTION OF EQUATION AND SOLUTION


Equation: . A statement in which values of two mathematical expressions are equal is called an equation sign of equal to is = equation with solution: Here we han find some solution for the given equation

X+5Y=2

X-12Y=10

From the above two equation we can find the value of two variable X, Y

equation with no solution:  a equation from which we cannot find the value of the variable is called any solution of equation.

X+Y=1

2X+2Y=2

From the above equation we cannot find the value of variable X,Y...since both the equations are same.to solve 2 variables we need two different equations. Having problem with Convert a Decimal to a Fraction keep reading my upcoming posts, i will try to help you.


Examples of no solution equation


Problem 1:4x-2+3x=3x+12+4x-14

Solution: 4x-2+3x=3x+12+4x-14

Step 1:  4x+2x-2=3x+4x+12-14

Step2:   7x-2=7x-2

Step 3:  7x-7x=-2+2

Step 4:  0=0

So there is no solution of this equation.

Problem 2:7x-4y+12z+4=5-3y+7x-y+12z

Solution:

Step 1:7x-4y-7x+3y+y+4=-12z+12z+5

Step2:0+4=0+5

Step 3:  4=5

So there is no solution of this equation.

Problem 3:

X+Y=2 (equation 1)

4X+4Y=8(equation 2)

Solution:

Step 1: multiply equation 1 by 4

Step 2: then we will get 4X+4Y=8

Step 3: now subtract this from equation 2

We will get 0=0

So there is no solution of this equation.