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) = and P(Y) = P() = and P() =
To Find: the probability that the assembled product will not be defective.
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)]
= 1- [P( X ) + P(Y ) + P( X Y)]
= 1- [P(X) P() + P(Y) P() + P(X) P(Y)]
= 1-[ + )+ ]
=1- + + ]
Therefore, The probability that the assembled product will not be defective is .
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