# Probability

• A measure of how likely it is that some event will occur
• Likelihood
• chance
• prospect
• odds
• possibility
• Improbability

# Probability - The Chance of Occurrence

Probability is all about expressing the chance of occurrence of an event on a one scale.

1. Question : How did you write your exams?

Reply : The paper was tough, I have a 60% chance of getting through.

Reply Reframed : The probability of me getting through the exam is 0.6

The event here is getting through the examination. The chance is 0.6.

2. Question : Will the principal give us permission to go on a picnic?

Reply : He is an understanding person. He knows and accepts the importance of picnics for children. There is a 95% chance that he may permit us.

Reply Reframed : The probability that the principal would permit us to go on a picnic is 0.95

The event here is the principal permitting the students to go on a picnic. The chance is 0.95

3. Question : I am tossing this coin. Can you say whether it will show up Heads or Tails?

Reply : The coin may show up either Heads or Tails. The chance of occurrence is equal for both heads and tails. 50% for Heads and 50% for tails.

Reply Reframed : The probability for the coin to show up heads is 0.5 and to show up tails is 0.5

The event here can be assumed in two ways

The event of getting a HEAD. The chance is 0.5

The event of getting a TAIL. The chance is 0.5

Reply Reframed : The probability for the coin not to show up heads is 0.5 and not to show up tails is 0.5

The event here can be assumed in two ways

The event of not getting a HEAD. The chance is 0.5

The event of not getting a TAIL. The chance is 0.5

4. Question : There are 10 balls in this bag, 4 of them red and 6 blue. I am picking up one ball. Will it be red or blue?.

Reply : The ball drawn may be either red or blue. Since all the balls have an equal chance of being drawn, there is a 4 out of 10 chance that the ball drawn is red and a 6 out of 10 chance that the ball drawn is blue.

Reply Reframed : The probability for the ball drawn to be red is 0.4

The event here is drawing a red ball. The chance is 0.4.

Reply Reframed : The probability for the ball drawn to be blue is 0.6

The event here is drawing a blue ball. The chance is 0.6.

# Occurrence - The three possibilities

When we think of something happening, we will come across three possibilities with regard to the chance of their occurrence.

# for Sure

It may happen for sure. We say it is certain.

If the chance of occurrence of the event is certain, you say that there is a 100% chance of it happening.

This expressed in probability terms would be "The probability of happening of the event is 1"

## Examples

1. Question : How did you write your exams?

Reply : I was very well prepared. There is no doubt at all. I have a 100% chance of getting through.

Reply Reframed : The probability of me getting through the exam is 1

2. Question : Will the principal give us permission to go on a picnic?

Reply : He is an understanding person. He knows and accepts the importance of picnics for children. He will permit us for sure. There is a 100% chance.

Reply Reframed : The probability that the principal will permit us to go on a picnic is 1

3. Question : There are 10 balls in this bag, all 10 of them blue. I am picking up two balls. Can you say whether the 2 balls would be blue or not.

Reply : What color would they be otherwise? Since all the balls are blue, you are sure to get 2 blue balls. There is a 100% chance that the 2 balls drawn are blue.

Reply Reframed : The probability for the balls drawn to be blue is 1

4. Question : I am throwing up a die. Can you say whether I would get any of the numbers 1,2,3,4,5,6 or not.

Reply : What else would appear? Since the six faces of the dice will have the numbers 1,2,3,4,5,6 on them, one of these should appear for sure. There is a 100% chance that one of the numbers 1,2,3,4,5,6 would appear.

Reply Reframed : The probability for the die to show up either 1,2,3,4,5 or 6 is 1.

# Never : Not at all

It may not happen at all. We say it is impossible.

If there is no chance of occurrence of the event, we say that there is a 0% chance of its happening.

This expressed in probability terms would be "The probability of the happening of the event is 0"

## Examples

1. Question : How did you write your exams?

Reply : Very bad. The paper was tough. I was not prepared for the exam. There is no doubt. I would fail. I have a 0% chance of getting through.

Reply Reframed : The probability of me getting through the exam is 0.

2. Question : Will the principal give us permission to go on a picnic?

Reply : There is a cyclone warning. How do you expect him to send us in such a situation. He will not permit us for sure. There is a 0% chance.

Reply Reframed : The probability that the principal will permit us to go on a picnic is 0.

3. Question : There are 10 balls in this bag, 4 of them white and 6 of them blue. I am picking up two balls. Can you say if I can draw a red ball or not.

Reply : What color would they be otherwise? Since all the balls are blue, you are sure to get 2 blue balls. There is a 100% chance that the 2 balls drawn are blue.

Reply Reframed : The probability for the balls drawn to be blue is 1.

4. Question : I am throwing up a die. Can you say whether I would get a multiple of 10 or not.

Reply : How can you expect to get the number 10 on the dice? The six faces of the dice will have the numbers 1,2,3,4,5,6 on them and only one of these should appear. There is a 0% chance that the number appearing is a multiple of 10.

Reply Reframed : The probability for the die to show up a multiple of 10 is 0.

# May or May not Happen

It may happen or may not happen. We say it is probable.

If the chance of occurrence of an event is uncertain, we say that there is a "x"% chance of it happening.

How much is "x"?

It would be dependent on the case in consideration.

This expressed in probability terms would be "The probability of it happening is p (=x ÷ 100)"

## Examples

The initial examples we have seen represent this state.

By probability we always mean the condition which is somewhere in between the two extremes of the event either happening for sure or not happening for sure.

Probability is a value which lies between the two extremes, 0 and 1 i.e. a positive value less than 1.

# 200%, 300%,.... 1000% Chance!!

What about those instances when we say I have a 200% chance or 500% chance etc.

They are wordings used to express the confidence with which you are expressing it and not numerical measures.

When something happens for sure, it is 100% and when it does not happen it is 0% and when it has a certain likelihood of occurrence somewhere in between these extremes it is between 0% and 100% and never 200% or 500% etc.

Something more than 100% in expressing the possibility of happening of an event should be understood as a qualitative measure rather than quantitative measure.