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,