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02 Nov 2021, 01:20
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Difficulty:
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Question Stats:
51% (02:37) correct
49%
(03:02)
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At an automotive plant, 2 % of cars produced have faulty braking systems. Each automobile undergoes a braking system check. When a car has a faulty braking system, this check correctly identifies the fault 90 % of the time. When a car does not have a faulty braking system, the check incorrectly identifies the system as faulty 5 % of the time. If the check reports that the braking system of a certain car is faulty, what is the probability that the braking system of this car is actually faulty?
A) \(\frac{9}{50}\)
B) \(\frac{18}{67}\)
C) \(\frac{41}{50}\)
D) \(\frac{49}{67}\)
E) \(\frac{499}{500}\)
A) \(\frac{9}{50}\)
B) \(\frac{18}{67}\)
C) \(\frac{41}{50}\)
D) \(\frac{49}{67}\)
E) \(\frac{499}{500}\)
07 Nov 2021, 23:44
Kudos
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nislam
At an automotive plant, 2 % of cars produced have faulty braking systems. Each automobile undergoes a braking system check. When a car has a faulty braking system, this check correctly identifies the fault 90 % of the time. When a car does not have a faulty braking system, the check incorrectly identifies the system as faulty 5 % of the time. If the check reports that the braking system of a certain car is faulty, what is the probability that the braking system of this car is actually faulty?
A) \(\frac{9}{50}\)
B) \(\frac{18}{67}\)
C) \(\frac{41}{50}\)
D) \(\frac{49}{67}\)
E) \(\frac{499}{500}\)
A) \(\frac{9}{50}\)
B) \(\frac{18}{67}\)
C) \(\frac{41}{50}\)
D) \(\frac{49}{67}\)
E) \(\frac{499}{500}\)
Probability (actually faulty) = Probability (faulty due to faulty braking system)/ [Probability (faulty due to faulty braking system) + Probability (faulty due to no faulty braking system)]
Probability (faulty due to faulty braking system) = 2/100 * 90/100 - 18/1000
Probability (faulty due to no faulty braking system) = 98/100 * 5/100 - 49/1000
Required probability = 18/(18 + 49) = 18/67
Option B
