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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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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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