Lesson Probabilistic analysis of testing procedures in industry

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Probabilistic analysis of testing procedures in industry


Problem 1

Ace  Machine  Works estimates that the probability its lather tool is properly adjusted is  0.8.
When the lathe is properly adjusted,  there is a  0.9  probability that parts produced pass inspection.
If the lathe is out of adjustment, however,  the probability of a good part being produced is only  0.2.
A part randomly chosen is inspected and found it to be acceptable.  At this point,
what is the posterior probability that the lathe tool is properly adjusted?

Solution


            In this problem, they want you find the  CONDITIONAL  probability,
            although they do not pronounce this term.

            They want you guess it   - - -   the correct guessing
            is a  PART  of the problem's solution  (and is its  MAJOR  part). 


So they want you find the conditional probability  

        P(lathe tool is properly adjusted given the randomly chosen part is acceptable).



In more formal way, they want you find 

       P(lathe tool is properly adjusted | the randomly chosen part is acceptable) = 


    = P(lathe tool is properly adjusted AND the randomly chosen part is acceptable) / P(the randomly chosen part is acceptable).



Regarding the numerator of this fraction, it is equal to

     P(lathe tool is properly adjusted AND the randomly chosen part is acceptable) = 0.8*0.9 = 0.72.



Regarding the denominator, it is equal to

    P(the randomly chosen part is acceptable) = 0.8*0.9 + (1-0.8)*0.2 = 0.76.



THEREFORE, combining these circumstances, we find the answer

    P(lathe tool is properly adjusted given the randomly chosen part is acceptable) = 0.72%2F0.76 = use your calculator = 0.9474 (rounded).



ANSWER.  The posterior probability that the lathe tool is properly adjusted  is equal to  0.9474,  or  94.74%.


My other lessons on  Probability  in this section are
    - Probabilistic analysis of a court verdicts
    - A company bids on two separate contracts
    - Advanced probability problems related to combinations
    - Using cumulative sums and relevant standard functions to solve problems on Binomial Distributions
    - Miscellaneous binomial distribution problems
    - Binomial distribution problems on overbooking flights
    - Advanced probability problems on binomial distribution
    - Accepting/rejecting shipments via acceptance procedures
    - Probabilistic analysis of testing procedures in health care
    - Probability problems on games
    - Probability problem on winning a many-rounds game
    - A Math circle level probability problem on a lottery game
    - Upper league entertainment probability problems
    - Upper league probability problems on Stars and Bars methodology
    - Upper league problem to maximize winning in a game with 20-sided rolling die
    - Upper league problems on conditional probability
    - Upper League geometric probability problems
    - Probability problems on long chains of related events
    - Probability problems similar to a coinciding birthdays problem
    - Using empirical rules to determine normal distribution probabilities
    - OVERVIEW of lessons on Probability, section 3


Use this file/link  OVERVIEW of lessons on Probability  to navigate over all my lessons on  Probability problems  (section 1)  in this site.

Use this file/link  OVERVIEW of my additional lessons on Probability  to navigate over all my lessons on additional  Probability problems  (section 2)  in this site.

Use this file/link  ALGEBRA-II - YOUR ONLINE TEXTBOOK  to navigate over all topics and lessons of the online textbook  ALGEBRA-II.


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