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.

Answer 1

Hint: Equate the part X that is not defective to a variable and do the same thing with Y as well and then find the intersection of the two cases.
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 $P\left( B \right) = \dfrac{{95}}{{100}}$
Required Probability is,
$P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right)$
$P\left( {A \cap B} \right) = \dfrac{{91}}{{100}} \times \dfrac{{95}}{{100}}$
$P\left( {A \cap B} \right) = \dfrac{{8645}}{{10000}}$
Note: We took 2 variables A and B as the non defective ones and then found the probability by taking the intersection of these 2 cases.