Introduction to Probability
A student is considering whether she should enroll in an MBA educational program offered by a well-known college. Among other things, she would like to know how difficult the program is she obtains the following marks distribution of students who appeared for the most final examination in the previous year.
Relative Frequency Distribution
|
Marks %
|
No. of students
|
% of students
|
|
0 - 25
|
45
|
8
|
|
25 - 50
|
280
|
50
|
|
50 - 75
|
205
|
37
|
|
75 - 100
|
30
|
5
|
|
|
560
|
100
|
Assuming the next exam is equally tough and there are same proportion of dull and bright students, she may conclude that the percentage of students in the four classes of marks will again be
|
Marks %
|
% of students
|
|
0 - 25
|
8
|
|
25 - 50
|
50
|
|
50 - 75
|
37
|
|
75 - 100
|
5
|
|
|
100
|
The first distribution above is related to past data and is a frequency distribution. The second distribution has the same numbers and is a copy of the first distribution. However, this distribution relates to the future. Such a distribution is called a probability distribution. Note the similarity of this distribution with that of the relative frequency distribution.
Hence by inspecting the probability distribution we can say that:
8% of the students who are appearing for the exam will score 0 - 25% marks, 50% will score 25 - 50% marks, 37% will score 50 - 75% marks and the balance 5% will score 75 - 100% marks.
If our student considers herself to be among the top 5% of the students, she can conclude that she will score 75 - 100% marks. If she considers herself to be in the top 42% of students she can conclude that she will score 50 - 100% marks and so on. However, if she has no idea of her ability in relation to the other students she can conclude that:
She has an 8% chance of scoring 0 - 25% marks, a 50% chance of scoring
25 - 50% marks, a 37% chance of scoring 50 - 75% marks and a 5% chance of scoring 75 - 100% marks. This "chance" is called probability in statistical language.
|
Probability theory is used to analyze data for decision making.
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The insurance industry uses probability theory to calculate premium rates. A stock analyst/investor, based on the probability estimates of economic scenarios and estimates the returns of the stocks. A project manager applies probability theory in decision-making.