Question 898179: I would like to know if I did the first question correctly and can you please walk me through how to solve the following two. I am trying to wrap my head around how to solve these types of questions. Here is the question:
A quality control officer at the THERMOS manufacturing plant performs three successive tests to find potential flaws in each completed thermos. The probability that the first test identifies a flaw is 0.05. The probability that the second test identifies a flaw is 0.2. The probability that the third test identifies a flaw is 0.1. To answer the following questions, assume that each of these tests is independent.
What is the probability that a thermos passes all three tests and makes it into a lunch box?
Law of total probability:
P[fail1] = .05 ⇒ P[pass1] = .95
P[fail2] = .2 ⇒ P[pass2] = .8
P[fail3] = .1 ⇒ P[pass3] = .9
Multiplication Principal ⇒ .95*.8*.9 = .684 ==> 68.4%
What is the probability that a manufactured thermos has exactly one flaw?
What is the probability that a manufactured thermos has more than one flaw?
Thank you for your time. -M
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A quality control officer at the THERMOS manufacturing plant performs three successive tests to find potential flaws in each completed thermos. The probability that the first test identifies a flaw is 0.05. The probability that the second test identifies a flaw is 0.2. The probability that the third test identifies a flaw is 0.1. To answer the following questions, assume that each of these tests is independent.
What is the probability that a thermos passes all three tests and makes it into a lunch box?
Law of total probability:
P[fail1] = .05 ⇒ P[pass1] = .95
P[fail2] = .2 ⇒ P[pass2] = .8
P[fail3] = .1 ⇒ P[pass3] = .9
Multiplication Principal ⇒ .95*.8*.9 = .684 ==> 68.4%
Correct
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What is the probability that a manufactured thermos has exactly one flaw?
P(only test 1 fail) = 0.05*0.8*0.9
P(only test 2 fail) = 0.2*0.95*0.9
P(only test 3 fail) = 0.1*0.95*0.8
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P(exactly 1 fail) = sum of above = 0.283
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What is the probability that a manufactured thermos has more than one flaw?
P(more than 1 fail) = 1 - P(none fail) = 1 - (0.95*0.8*0.9) = 0.316
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Cheers,
Stan H.
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