Q256 / 270 · NDA 2018 (Phase 2) · Mathematics

In a bolt factory, machines $\mathrm{X}, \mathrm{Y}, \mathrm{Z}$ manufacture bolts that are respectively $25 \%, 35 \%$ and $40 \%$ of the factory's total output. The machines X, Y, 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 ?

  • Correct answer
    A
    5/39
  • B
    11/39
  • C
    20/39
  • D
    34/39

Solution

Required probability $=\frac{25 \times 2}{25 \times 2+35 \times 4+40 \times 5}=\frac{5}{39}$

Hence, the correct answer is option: 'A'.

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