Probability :: What it is?

Probability

• Meaning

  A measure of how likely it is that some event will occur

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• Synonyms

  Likelihood, chance, prospect, odds, possibility.

• Antonyms

  Improbability.

Probability and relevant Terms

Probability is all about expressing the chance of occurrance 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 for going 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.

   The probability that the principal will permit us to go on a picnic is 0.95

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

   Reply: The coin may show up either Heads or Tails. Both have a equal chance of occurance. 50% for Heads and 50% for tails.

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

   The probability for the coin not to show up heads is 0.5 and not to show up tails 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. Can you say whether it would 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.

   The probability for the ball drawn to be red is 0.4

   The probability for the ball drawn to be blue is 0.6

The three possibilities

When we think of something happening, we will come across three possibilities.

1. For Sure

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

   If the chance of occurance 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 it happening is 1"

   Eg:

   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 for going 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.

      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.

      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.

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

2. Never: Not at all

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

   If the chance of occurance of the event is impossible, you say that there is a 0% chance of it happening. This expressed in probability terms would be "The probability of it happening is 0"

   Eg:

   1. Question : How did you write your exams?

      Reply : Very bad. The paper was tough. I was not prepare 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 for going 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.

      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: How do you expect to draw a red ball when there is no red ball in the bag? You cannot draw a red ball at all. There is a 0% chance for the ball drawn to be red.

      The probability for the ball drawn to be red is 0.

   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.

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

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3. May or May not Happen

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

   If the chance of occurance of the 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)"

   Eg:

   The examples that we have first seen would represent this. By probability we always mean this condition which is somewhere in between the two extremes of the event either happening for sure or not happening for sure. The probability is a value which lies between the two extremes, 0 and 1. This shows that it is a positive value less than 1.

200%, 300%,.... 1000%

What about those instances when we say I have a 200% chance or 500% chance etc. Those are wordings used to express the confidence with which you are expressing it and not a 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 occurance 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.

Author Credit : The Edifier

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