Introduction
Probabilities and likelihoods are everywhere around us, it is used in:
(1) Weather forecasting
(2) Games
(3) Insurance
(4) Election polls etc.
However, in the history of mathematics, probability is actually a very recent idea. While numbers and geometry were studied by ancient Greek mathematicians more than 2500 years ago, the concepts of probability only emerged in the 17th and 18th century.
According to legend, two of the greatest mathematicians,
To distract from the difficult mathematical theories they were discussing, they often played a simple game: they repeatedly tossed a coin every heads was a point for Pascal and every tails was a point for Fermat. Whoever had fewer points after three coin tosses had to pay the bill.
One day, however, they get interrupted after the first coin toss and Fermat has to leave urgently.
Later, they wonder who should pay the bill, or if there is a fair way to split it.
The first coin landed heads (a point for Pascal), so maybe Fermat should pay everything. However, there is a small chance that Fermat could have still won if the
When we speak of a coin, we assume it to be ‘fair’, that is, it is symmetrical so that there is no reason for it to come down more often on one side than the other.
We call this property of the coin as being ‘unbiased’. By the phrase ‘random toss’, we mean that the coin is allowed to fall freely without any bias or interference
Pascal and Fermat decided to write down all possible ways the game could have continued:
All four possible outcomes are equally likely, and Pascal wins in
Thus, they decided that Fermat should pay