# Consider the case of a manufacturer who has an automatic machine that produces an important part. Pa

Discussion in 'Calculator Requests' started by math_celebrity, Jan 7, 2017.

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1. ### math_celebrityAdministratorStaff Member

Consider the case of a manufacturer who has an automatic machine that produces an important part. Past records indicate that at the beginning of the data the machine is set up correctly 70 percent of the time. Past experience also shows that if the machine is set up correctly it will produce good parts 90 percent of the time. If it is set up incorrectly, it will produce good parts 40 percent of the time. Since the machine will produce 60 percent bad parts, the manufacturer is considering using a testing procedure. If the machine is set up and produces a good part, what is the revised probability that it is set up correctly?

Determine our events:
• C = Correctly Set Machine = 0.7
• C|G = Correctly Set Machine And Good Part = 0.9
• I = Incorrectly Set Machine = 1 - 0.7 = 0.3
• I|G = Incorrectly Set Machine And Good Part = 0.4
• B< = BAD PARTS = 0.60

P[correctly set & part ok] = P(C) * P(C|G)
P[correctly set & part ok] = 70% * 90% = 63%

P[correctly set & part ok] = P(I) * P(I|G)
P[incorrectly set & part ok] = 30% *40% = 12%

P[correctly set | part ok] = P[correctly set & part ok]/(P[correctly set & part ok] + P[incorrectly set & part ok])
P[correctly set | part ok] = 63/(63+12) = 0.84 or 84%
The text passage contains a detailed probability problem and provides a solution to the question asked.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# Consider the case of a manufacturer who has an automatic machine that produces an important part. Pa

Discussion in 'Calculator Requests' started by math_celebrity, Jan 7, 2017.

Tags:
1. ### math_celebrityAdministratorStaff Member

Consider the case of a manufacturer who has an automatic machine that produces an important part. Past records indicate that at the beginning of the data the machine is set up correctly 70 percent of the time. Past experience also shows that if the machine is set up correctly it will produce good parts 90 percent of the time. If it is set up incorrectly, it will produce good parts 40 percent of the time. Since the machine will produce 60 percent bad parts, the manufacturer is considering using a testing procedure. If the machine is set up and produces a good part, what is the revised probability that it is set up correctly?

Determine our events:
• C = Correctly Set Machine = 0.7
• C|G = Correctly Set Machine And Good Part = 0.9
• I = Incorrectly Set Machine = 1 - 0.7 = 0.3
• I|G = Incorrectly Set Machine And Good Part = 0.4
• B< = BAD PARTS = 0.60

P[correctly set & part ok] = P(C) * P(C|G)
P[correctly set & part ok] = 70% * 90% = 63%

P[correctly set & part ok] = P(I) * P(I|G)
P[incorrectly set & part ok] = 30% *40% = 12%

P[correctly set | part ok] = P[correctly set & part ok]/(P[correctly set & part ok] + P[incorrectly set & part ok])
P[correctly set | part ok] = 63/(63+12) = 0.84 or 84%
user
The text passage contains a detailed probability problem and provides a solution to the question asked.

TYPE: SINGLE_QUESTION_WITH_ANSWER