The mathematical theory of probability was discovered by two Frenchmen: Blaise Pascal and Pierre Fermat. Although gambling was the first to play a major role in the applications of probability, the subject has evaded the entire universe. In recent times, almost everything is described in terms of probabilities.
As we find that day-to-day life is full of uncertainities, there arises a critical need to measure these uncertainities to reach a certain point. Probability can be described as the science of measuring uncertainities. It is a numerical representation of an abstract situation.
The three main methods adopted to measure probability of the occurance of an event are:
1) Relative frequency approach:
The frequency of the event is divided by the sample size.
2) Subjective or intuitive approach:
When required data about the event is unavailable, the probability is measured completely on previous experience, belief or intuition.
3) Classical approach:
The number of outcomes favourable to the event is divided by the total number of outcomes.
Facts of probability:
1) The probability of an event A is denoted by P(A).
2) The value always lies between 0 (0% chance) and 1 (100% chance).
3) The sum of probabilites of related events in an experiment is always 1.
Note: The sum of probabilities of occurance & non-occurance of an event is also 1. Let p & q be the probabilities of occurance & non-occurance of an event. Then p+ q = 1. This implies q = 1 - p.
Let us consider a few examples:
1. Kris told Joe the probability of her car starting tomorrow morning is just about 0.
a) What method did Kris use for assigning this probability to the event that her car will start?
b) If Kris is correct and the probability of her car starting is close to 0, would you say the car is likely to start or not? What would you say if the probability were close to 1?
Ans: a) Kris has used the subjective or intuitive method to assign the probability.
b) As 0 represents no occurance of the event, it is very clear that the car is not likely to start. As 1 represents 100% occurance of the event, with probability 1, it can be said that the car will definitely start.
2. The city council has three liberal members (one of whom is the mayor) and two conservative members. One member is selected at random to testify in Washington, D.C.
a) What is the probability this member is liberal?
b) What is the probability this member is conservative?
c) What is the probability the mayor is chosen?
Ans: Based on the data, the Classical method would be the best.
a) P (member is liberal) = 3/5
b) P (member is conservative) = 2/5
c) P (mayor) = 1/5.
