At an automotive plant, 2 % of cars produced have faulty braking syst

Question

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}

Abhishekgmat87 · Answer

Probability (actually faulty) = Probability (faulty due to 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

nislam · Answer

could any one please provide the detail solution of the math?

ThatDudeKnows · Answer

nislam

Is there a piece of information that you would just LOVE to know that's missing from the question? What if we knew the total number of cars? Wouldn't knowing that make our lives much easier? Then let's make it up!! (I call these Hidden Plug In questions, and if you search for ThatDudeKnowsHiddenPlugIn, you'll find other examples.)

Let's say there are 1000 cars.
2% have faulty braking systems, so 20. The check correctly identifies 90%, so 18, of those. 18 times we're told there is a problem and there actually is a problem.
When a car does not have a faulty braking system (that's 980 cars), 5% of those say there is a problem. 5% of 980 is 49. 49 times we're told there is a problem and there actually is NOT a problem.
There is a total of 18+49=67 times when we are told there is a problem. Of those, 18 times there is actually a problem.
16/67
Answer choice B.

ThatDudeKnowsHiddenPlugIn

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

At an automotive plant, 2 % of cars produced have faulty braking syst

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

At an automotive plant, 2 % of cars produced have faulty braking syst

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards