Question

Provide an example of what differentiates a "probability" from a "Probability Distribution". In this example identify both the probability and the probability distribution.

Answer 1

PROBABILITY:

Probability describes a persons assessment of the likelihood of occurrence of a particular outcome. It is expressed as a number between 0 and 1; a 0 indicates an impossible outcome; a 1 indicates that an outcome is certain to occur;

PROBABILITY DISTRIBUTION:

A random process can be described by one or more variables or attributes, and its outcomes by their numerical values or categories. Such variables or attributes will be referred to as random variables or random attributes.

A probability distribution is a list showing the possible values of a random variable (or the possible categories of a random attribute) and the associated probabilities.

EXAMPLE:

Let us consider an example of tossing a coin.

The number of possible outcomes are: {Head, Tail}

Suppose X be the event of getting head.

Therefore the chance of getting head =1/2

Hence, The probability is nothing but a chance of occurrence of a particular event out of the total event.

And how this probability for the different event distributed are known to be a probability distribution. It is a list showing the possible values of a random variable and the associated probabilities. Hence the probability distribution of random variable X (event of getting head) is given by:

X (Event of getting Head)	Associated Probability [P(X)]
0	0.5
1	0.5