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Subjective Probability

This is another way to interpret probabilities using personal evaluation of an event. If the odds in favor of A are a : b then the subjective probability is taken as P(A) = a/(a+b).

If the odds against A are a : b then the subjective probability is taken as P( A) = b/(a+b).

These subjective probabilities may or may not satisfy the third axiom of probability.


Example 7. An article manufactured by a company consists of two parts I and II In the process t1{ manufacture of part L 9 out of 100 are likely to be defective. Similarly, 5 out of 100 are likely 10 be defective in the manufacture of part II. Calculate the probability that the assembled article wil1 not be defective.


             Solution. Here the assembled article will not be defective means both the parts I and II will not be defective.


P( defective part I) = 9/100

                                   P (non-defective part I) = 1-(9/100) = 0.91

P (defective part II) = 5/100

P (non-defective part II) = 1- (5/100) = 0.95


Since the manufacturing of part I and part II are independent then P (assembled article will not defective)

= P (non-defective part I). P (non-defective part II)

= (0.91) (0.95) = 0.8645.

Example 8. Six men in a company of 15 are engineers. If 3 men are picked out of the 15 at what is the probability of at least one engineer ?

Solution. The event 'at least one engineer' can be split up into three mutually exclusive events :

(i) exactly 1 engineer and 2 non-engineers

(ii) exactly 2 engineers and 1 non-engineer

(iii) exactly 3 engineers and 0 non-engineer.

The probabilities of these cases are respectively,

By the theorem of total probability we obtain,