#classicalapproachofprobability

The scene that you saw shows Tia confessing to Jazz Singh (played by Saif Ali khan) that he could be her father. Jazz Singh’s intentions seem very different towards Tia while she is narrating a story that her mother told her. Her mother mentioned that there were 3 men in her life (options) and either of them could be her father. Tia finally tells Jazz that there is a 33.33% chance that Jazz is her father. This revelation leaves him aghast.

In this blog, Learning Perspectives will explore the meaning of Probability.

What is the meaning of Probability?

Probability is a numerical value that represents the chance, likelihood, possibility that an event will occur (always between 0 and 1).  The concept of probability was developed by Jacob Bernoulli, Thomas Baye. It was later refined by many others including Laplace. Earlier, probability was applied mostly on gambling tables. Later, it was discovered that it can be applied to social, economic, political and business problems as well.

A classic example to understand probability is when a deck of cards is shuffled, probability of getting each card is 1/52. There are 52 cards in a playing deck, hence when we draw any random card, likelihood of drawing that card would be one divided by fifty two. [Denominator indicates total number of cards]

Similar to the scene that we saw, if there are 3 options (Men, in this case) and only one can be Tia’s  father, hence probability is 1/3 or 33.333%. [denominator indicates the total no. of men]

Deep understanding of probability helps business owners to deal with uncertainty in finding business solutions. They can assess risks involved in each alternatives and eventually minimize risk.

Classical approach:

This approach was the earliest in probability. This school of thought says that outcomes of an experiment have equal odds of happening. For example: from a well shuffled deck of cards, probability of  drawing a heart is 13/52=1/4. There are 13 cards each of heart, spades, clubs and diamonds. Probability of drawing a black card would be 13*2= 26; 26/52=1/2 [ Spades and Clubs are black while hearts and diamonds are red].

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Empirical approach:

This approach is based on observed data. For example: we want to know how many times a head will turn up if we toss a coin 1000 times. We toss a coin 1000 times and then we can draw our answer based on the observations of our experiment.

If an experiment is performed n times under the same conditions and there are ‘a’ outcomes. a<=n, favoring an event, then an estimate of the probability of that event is the ration a/n

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One should understand that we might never obtain the probability of an event as given by the above limit. We can try to have a close estimate of P (E) based on large n. However this approach does emphasis that probability involves a long run concept.

Subjective approach:

This approach is solely based on the intuition of a person. It is vague and rarely accurate. For example: On a particular day, a person might feel that there is a 40% probability that it will rain on that day.

Though these are different schools of thoughts, there is no conflict on foundation of probability at mathematical level as each school defines probability as ration or a proportion. Any approach can be used depending on the problem.

Tia used the classical approach, when she considered equal likelihood of either of them being her father. A probability of 1/3 or 33.333%.

Written by: Ms. Gitika Chandra