Probability Line - Definition, Basic Probability & Expected Value

# Probability Line

What is the probability of getting a $12$ when a dice is rolled? Definitely zero as it is not possible. Probability is defined as likelihood or chance of happening of an event. An event can be ranged from an impossible event to a sure event. Some events are unlikely to happen though not impossible while others are more likely to happen. The probability line will range from $0$ to $1$ as the probability of an event cannot be less than zero or more than one.

## Definition

Probability line is a kind of number line where the probabilities of an event is represented. An event can be categorized as impossible, unlikely, likely and sure event based on the probability obtained. For example, what is the probability that your father is elder than you in age $1$, that is, it is sure to happen. The probability of any event will lie between $0$ to $1$.
1) If the event is having probability $0$ then it is an impossible event.

2) If the event has a probability of $1$ then it is a sure event.

## Basic Probability

Probability of an event is defined as the number of favorable events to the total number of events in the sample space. For an event $E$, if number of favorable events is $n(E)$ and total number of events are $n(S)$, then the probability of the event $E,\ P(E)$ will be written as:
$P(E)$ = $\frac{n(E)}{n(S)}$

The probability can be categorized as given here:

1) If probability is zero, then it is an impossible event.

2) If probability is greater than zero and less than $0.5$, then event is unlikely.

3) If probability is greater than $0.5$ and less than $1$, then event is likely.

4) If probability is equal to $1$, then it is a sure event.

## Expected Value

For a random experiment, the expected value of an event is the mean of all the probabilities. The expected value of a discrete random variable $X$ is the sum of product of different values and their probabilities, if it exists. For a continuous variable the expected value is the interval of the product of probability density function and continuous variable $X$ over the set of real numbers.

## Showing Probability on Probability Line

Given is the probability line. It ranges from $0$ to $1$. The event lying on the leftmost side are more unlikely to happen than those lying on the right side.

This line shows the possible probabilities of an event. If the probability is coming towards left side of the line then the event is more unlikely to happen and if the probability is approaching the right side of the line then the event is likely to happen.