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Subjective Probability

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When learning about Independent event, one will understand the importance of two events in one sample space. Subjective probability is based on a personal evaluation in favor of that independent favor when trying to measure various probabilities. Subjective probabilities may not cooperate with third axiom of probability.

So here weâ€™ll suppose things are positively working out in favor of A and positioning a : b condition: P(A) = a/(a+b). If the opposite situation occurs, where things are positioning a negative circumstance and quite against A with a : b then weâ€™ll get P( A) = b/(a+b).

Let us consider this following example and get the measure the subjective probability:

Six men in a company of 15 are engineers. If 3 men were picked out of the 15, then calculate probability of at least one engineer?

Solution:

Here 3 men were picked out of 15 where if weâ€™ll separate minimum one engineer in each group and then measure weâ€™ll get these three cases:

• 1 engineer and 2 non-engineers
• 2 engineers and 1 non-engineer
• And 3 engineers and 0 non-engineer

So weâ€™ll get these three separate cases of probabilities:

(6/1) (9/2)/ (15/3) = 216/455,Â Â  (6/2) (9/1)/ (15/3) = 135/455, (6/3) (9/0)/ (15/3) = 20/455

Hence weâ€™ll get the answer:

P ( at least one engineer) = 216/455 + 135/455 + 20/455 = 371/455

Here is another example to consider:

An article manufactured by a company consists of two parts I and II. In the process t1 manufacture of part L, 9 in the total of 100 are stated as defective. Similarly, 5 in total of 100 are stated as defective in the manufacture of part II. Calculate probability that assembled article will not have any defective pieces.

Solution:

The first thing to point out is that there is a mention of defective part both in part I and II and we have to calculate the part thatâ€™ll not be defective.

So, first part I: P( defective part I) = 9/100

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

P (defective part I) = 5/100

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

Now comes the part where we describe Part I and II as independent events then

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

So weâ€™ll place:

(0.91) (0.95)

= 0.8645

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