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 $A=PartX$ is not defective.
Probability of $A$ is $P\left(A\right)={\displaystyle \frac{91}{100}}$
Similarly for $B$,
$B=PartY$is not defective
Probability of $B$ is $P\left(B\right)={\displaystyle \frac{95}{100}}$
Required Probability is,
$P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$
$P\left(A\cap B\right)={\displaystyle \frac{91}{100}}\times {\displaystyle \frac{95}{100}}$
$P\left(A\cap B\right)={\displaystyle \frac{8645}{10000}}$
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.