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Question
An article manufactured by a company consists of two parts X and Y. In the process of manufacture of the part X, 9 out of 100 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part Y. Calculate the probability that the assembled product will not be defective.
Solution
\[\text{ Let} : \]
\[A = \text{ Particle X is defective} \]
\[B = \text{ Particle Y is defective } \]
\[ \therefore P(A) = \frac{9}{100}\]
\[ P(B) = \frac{5}{100}\]
\[\text{ Required probability } = P\left( \bar{A} \cap \bar{B} \right)\]
\[ = P\left( \bar{A} \right) \times P\left( \bar{B} \right)\]
\[ = \left[ 1 - P\left( A \right) \right] \times \left[ 1 - P\left( B \right) \right]\]
\[ = \left[ 1 - \frac{9}{100} \right] \times \left[ 1 - \frac{5}{100} \right]\]
\[ = \frac{91}{100} \times \frac{95}{100}\]
\[ = 0 . 91 \times 0 . 95\]
\[ = 0 . 8645\]
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