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 part $Y$.Calculate the probability that the assembled product will not be defective.

Let $A = Part X$ is not defective.
Probability of $A$ is $P\left( A \right) = \dfrac{{91}}{{100}}$
Similarly for $B$,
$B = Part Y$is not defective
Probability of $B$ is $P\left( B \right) = \dfrac{{95}}{{100}}$
$P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right)$
$P\left( {A \cap B} \right) = \dfrac{{91}}{{100}} \times \dfrac{{95}}{{100}}$
$P\left( {A \cap B} \right) = \dfrac{{8645}}{{10000}}$