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# Probability Line

Probability is defined as the likelihood of occurrence of an event. The probability of any event can lie between 0 and 1. The probability of an event is the ratio of a number of favorable events to the total number of events. The probabilities of different events can be represented and compared on a line marked from 0 to 1, known as a probability line or probability scale. There are different types of events - mutually exclusive, independent, dependent, exhaustive, and many others- whose probabilities can be calculated based on different rules of probability.

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## Definition

The representation of the probability of events on a number line which starts from zero and ends at 1 is known as a probability line. The probability line can be used to represent the likelihood of an event as given below:

1. Impossible event: At 0 on the probability line, an event is an impossible event.

2. Certain event: At 1 on the probability line, an event is a certain event or sure event.

3. Even chance event: At 0.5 on the probability line, the event has even chances or occurring or not occurring.

4. Unlikely chances: In the probability line, events lying between 0 and 0.5 are unlikely events.

5. Likely chances: In the probability line, events lying between 0.5 and 1 are likely events.

## Probability scale

The probability scale varies from 0 to 1. The probability of an event cannot be less than zero or greater than 1. The more an event is nearer to zero, more unlikely it is. Similarly, more an event is nearer to one more likely it is. Here is the probability line divided into five parts.

There are few events as given below and we have to mark them on a probability scale.

A: The sun will not rise tomorrow.

B: The sun will rise tomorrow.

C: A head will come if a coin is tossed.

Let us see how they can be marked on the probability scale.

## Examples

Example 1: Arrange the given statements in an order where the more likely event is followed by the less likely event.

a. If the football match score is 10-1, then the team scoring 10 goals will win.

b. Penguin to survive in Africa.

c. There will not be mathematics as a subject is my school.

d. A baby will be born in China today.

Solution: The events are ordered as given below.

MORE LIKELY to LESS LIKELY

A baby will be born in China today.

If the football match score is 10-1, then the team scoring 10 goals will win.

There will not be mathematics as a subject is my school.

Penguin to survive in Africa.
Example 2: There are 2 red balls and 5 green balls in a bag. Rate the given events on the probability scale.

a. If one ball is chosen at random, it will be a red ball.

b. If one ball is chosen at random, it will be a black ball.

Solution: The probabilities can be calculated as given below.

a. Probability of getting a red ball = $\frac{2}{7}$

b. Probability of getting a red ball = $\frac{5}{7}$

Example 3: Given are four events on a probability scale. Rate them in the order from least likely to most likely.

Solution: A probability line ranges from 0 to 1, where 0 is represented at the leftmost point and 1 at the rightmost point.

The ranking of events from least likely to most likely is B, A, C, D.
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