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In a factory, two machines $M1$ and $M2$ manufacture $60\%$ and $40\%$ of the autocomponents respectively. Out of the total production $2\%$ of $M1$ and $3\%$ of $M2$ are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by $M2$?

  1. $0.35$
  2. $0.45$
  3. $0.5$
  4. $0.4$
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