Learning Dice Probability

Dice Probability is simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all cases possible. In this classic conception of dice probability we would say that an object is chosen at random out of a given class, if the condition in this section allows us to give the same of dice probability for any other member of this class.

Before you play any dice game it is good to know the probability of any given total to be thrown. First let’s look at the possibilities of the total of two dice. The table below shows the six possibilities for die 1 along the left column and the six possibilities for die 2 along the top column. The bodies of the table show the sum of die 1 and die 2.

The colors of the body of the table illustrate the number of ways to throw each total. The probability of throwing any given total is the number of ways to throw that total divided by the total number of combination (36). In the following table the specific number of ways to throw each total and the probability of throwing that total is shown.

The following shows the probability of throwing each total in a chart format. As the chart shows the closer the total is to 7 the greater is the probability of it being thrown.

Hope this is helpful please leave a comment in case you need any clarification.

Division

Division is one of the arithmetic operations. Division is the inverse form of multiplication. The term division is sometimes said to be sharing.


Division is often shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a Vinculum or Fraction Bar, between them. For example, a divided by b is written

This can be read out loud as "a divided by b", "a by b" or "a over b". A way to express division all on one line is to write the dividend, or numerator then a slash, then the divisor, or denominator like this:

The Division facts for Two and Three are listed in the below table:

TWO

0/2 = 0	2/2 = 1	4/2 = 2	6/2 = 3	8/2 = 4
10/2 = 5	12/2 = 6	14/2 = 7	16/2 = 8	18/2 = 9

THREE

0/3 = 0	3/3 = 1	6/3 = 2	9/3 = 3	12/3 = 4
15/3 = 5	18/3 = 6	21/3 = 7	24/3 = 8	27/3 = 9

Binomial Random Variables

Binomial Random variables help us to make a link between probability and numbers that we observe as data.

Binomial Random Variable: A numerical valued function defined on a sample space. A random variable X “maps” an outcome in a sample space to a numerical value. We use capital letters such as X or Y to denote binomial random variables. Let s be an elementary outcome. A value, X(s), of X is denoted x.

A binomial random variable is discrete if it can take on a finite or countable number of values. A continuous random variable takes on an uncountable number of values.
Binomial Random Variable:

General features of a Binomial Random Variable:

* The binomial random experiment consists of n identical trials.
* Possible outcomes on each trial are of only two. given one outcome by S (for Success) and the other by F (for Failure).

* The probability for Success(S) remains the same from trial to trial. Denote it by p=Pr(Success).

* The trials of binomial random experiment are independent of each other.

* Then we say Binomial Random Variable X as the number of Successes in n trials.

Counting Principles

All branches of mathematics are having their own fundamental theorems. Fundamental theorems are considered as an important base in following the rest of the materials. Let us consider some of the fundamental theorems or principles that are used. They are of three types of counting principles as follows,

1. Fundamental theorem of arithmetic
2. Fundamental theorem of algebra
3. Fundamental theorem of linear programming.

Fundamental Counting Principles:

In fundamentals of arithmetic every integer that are greater than one, either prime or composite can be expressed as an only one of its kind product of prime numbers.

In fundamentals of algebra every polynomial which have degree greater than 0 must produce the result as one real or complex number.

In fundamentals of linear programming the result occur at single corner point or between two corner points of a line segment, if only linear programming problems are having any solutions.