#probability basics

Previously we have discussed about antiderivative trig functions and In today's session we are going to discuss about Probability and its basics which is a part of karnataka state board sslc syllabus.

In everyday life, we come across statements such as :-

- Most probably it will rain today.

- Chances are high that the price of petrol will go up.

- I doubt that he will win the race.

The words ' most probably ', ‘chances’, 'doubt ' etc. show uncertainty or probability of occurrence of an event.

Here we will discuss History of Probability. The origin of the subject can be traced in the equivalence between two French mathematicians B Pascal (1623 – 1662 ) and Pierre de Fermat (1601 – 1665 ). In 1654, a French nobleman and gambler Charles Mere asked Pascal to solve certain dice problems. Pascal solved these problems in collaboration with Fermat.

Dutch scientist Huygens (1629 – 1695 ) wrote the first book on probability.

-In 1713, A more comprehensive book was written by J Bernoulli.

-In 1748, A De Moivre published his book ' The Doctrine of Chances'.

-In 1812, Laplace published his book 'Analytic Theory of Probability'.

In the 20th centuries, important contributions were made by Russian mathematician. A A Markov and A N Kolmogorov.

These days, probability theory is extensively used in various fields.

Probability basics or terms are :-

-Experiment :- An activity which ends in some well defied outcomes. For example, drawing a ball from a bag

-Random Experiments :- An experiment in which all outcomes are known in advance but the exact result of any specific trial cannot be surely predicted . For example, tossing a coin

-Trial :- Performing an experiment once.

-Event :- The Possible outcomes of a trial. For example, when a coin is tossed the occurrence of Head or Tail is an event.

-Equally Likely Events :- If the different outcomes have same occurrence.

-Exhaustive Events :- The total number of all possible outcomes.

-Mutually Exclusive Events :- Two events in an experiment.

-Favorable Events :- The cases which ensure the occurrence of an event.