Question

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.

Answer 1

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\(\frac{437}{500}\).