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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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