# An article manufactured by a company consists of two parts X and Y. In the process of manufacture of part X.

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An article manufactured by a company consists of two parts X and Y. In the process of manufacture of part X. 8 out of 100 parts may be defective. Similarly, 5 out of 100 parts of Y may be defective. Calculate the probability that the assembled product will not be defective.

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Given: X and Y are the two parts of a company that manufactures an article.

Here the probability of the parts being defective is given i.e,

P(X) = $\frac{8}{100}$ and P(y) = $\frac{5}{100}$

$\Rightarrow$ P($\overline x$) = $\frac{92}{100}$ and P($\overline y$) = $\frac{95}{100}$

To Find: the probability that the assembled product will not be defective.

Here,

P(product assembled will not be defective)

= 1 – P(product assembled to be defective)

=1 – [P(X and not Y) + P(Y and not X) + P(both)]

$\frac{437}{500}$

Therefore, The probability that the assembled product will not be defective is$\frac{437}{500}$.