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In a bolt factory, machines X, Y, Z manufacture bolts that are respectively $25 \%, 35 \%$ and $40 \%$ of the factory's total output. The machines $\mathrm{X}, \mathrm{Y}, \mathrm{Z}$ respectively produce $2 \%, 4 \%$ and $5 \%$ defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?
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Verified Answer
The correct answer is:
$\frac{5}{39}$
Required probability
$=\frac{25 \times 2}{25 \times 2+35 \times 4+40 \times 5}=\frac{5}{39}$
$=\frac{25 \times 2}{25 \times 2+35 \times 4+40 \times 5}=\frac{5}{39}$
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