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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. $0.720$
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Best answer

B.

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

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

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

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4 Comments

@

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

The chosen shock absorber is already been found to reliable which means we should restrict the sample space to reliable ones only....and from these reliable ones we have to look for Y being reliable!

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@jatin khachane 1 finding reliable one from X and Y is nothing but total probability.

Given that what we found is reliable, what is the probability it is from Y => Baye's theorem. So yes it is based on Baye's theorem.

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@ Arjun sir

Why is the answer  not . Option C ( .667)

 According to Bayes' theorm first select which observer X and Y .. so probability  ( .5 )   then apply condition

 Plz tell me sir
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