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An automobile plant contracted to buy shock absorbers from two suppliers $ X$ and $ Y$ . $ X$ supplies $60\%$ and Y supplies $40\%$ of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $ X’s$ shock absorbers, $96\%$ are reliable. Of $ Y’s$ shock absorbers, $72\%$ are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by $Y$ is

  1. $0.288$
  2. $0.334$
  3. $0.667$
  4. $0.720$
asked in Numerical Ability by Boss (18.3k points)
retagged by | 954 views

1 Answer

+20 votes
Best answer

B.

Then by using Bayes' Theorem :
$\text{Probability of Y given R} = \dfrac{\text{Probability of Y and R}}{\text{Probability of R}}$

$= \dfrac{0.4 \times 0.72}{0.4 \times 0.72 + 0.6 \times 0.96}$

$= \dfrac{1}{3} = 0.33$

answered by Active (3.5k points)
edited by
0

@Arjun Sir, 

@Bikram Sir,

Why the answer is not a) 0.288

I think this calculation is suitable when we have given in question 

The probability that a randomly chosen reliable shock absorber, which is found to be reliable, is made by Y is
 

but in the question they have asked:-

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is
 

 Means among randomly choosen (whether it could be reliable or unreliable or whether it is of X or of Y).

So the denomenator part should be calculated as:-

0.6*0.96 (from x and reliable)+ 0.6*0.04(x and unreliable) + 0.4*0.72(from y and reliable) + 0.4*0.28(from y and unreliable)

which is equal to 1

and Numerator as 0.4*0.72(from y and reliable)

which is 0.288

what is wrong in this.??

0
@shubhanshu

even i got 0.288
0
Question has asked about the reliable ones ..
0

Yes question is asking about reliable only

But in the question, it is nowhere written that Probability to select Reliable shock absorber from Y out of All reliable shock absorbers.

0

@shubhanshu

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

i think this statement wants us to find Y out of reliable ones

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