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  • In a bolt factory, machines A, B and C manufacture respectively 20%, 30% and 50% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random f

In a bolt factory, machines A, B and C manufacture respectively 20%, 30% and 50% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random form the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine C is.

Option: 1

\frac{5}{14}


Option: 2

\frac{3}{7}


Option: 3

\frac{9}{28}


Option: 4

\frac{2}{7}


Answers (1)

best_answer

\begin{aligned} & \mathrm{P}(\mathrm{A})=\frac{2}{10} \mathrm{P}(\mathrm{B})=\frac{3}{10} \mathrm{P}(\mathrm{C})=\frac{5}{10} \\ & \mathrm{P}(\text { Defective } / \mathrm{A})=\frac{3}{100}, \mathrm{P}(\text { Defective } / \mathrm{B})=\frac{4}{100}, \mathrm{P}(\text { Defective } / \mathrm{C})=\frac{2}{100} \\ & \mathrm{P}(\mathrm{E})=\frac{5 / 10 \times 2 / 100}{\frac{2}{10} \times \frac{3}{100}+\frac{3}{10} \times \frac{4}{100}+\frac{5}{10} \times \frac{2}{100}}=\frac{10}{6+12+10} \\ & =\frac{10}{28} \\ & =\frac{5}{14} \end{aligned}

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Divya Prakash Singh

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