Question

An article manufactured by a company consists of two parts X and Y. In the process of manufacture of part X, 9 out of 104 parts may be defective. Similartly, 5 out of 100 are likely to be defective in the manufacture of the part Y. Calculate the probability that the assembled product will not be defective.

• A. $\frac{360}{416}$
• B. $\frac{331}{416}$
• C. $\frac{361}{416}$
• D. $\frac{324}{416}$

Answer 1

The correct option is C

$\frac{361}{416}$

Since in the process of manufacture fo part X, 9 out of 104 part may be defective, therefore the probability of x to be defective$=\frac{9}{104}$ and
its not being defective $=1-\left(\frac{9}{104}\right)=\frac{95}{104}.$
Similartly the probability of the part Y to be defective $=\frac{5}{100}=\frac{1}{20}$and
not to be defective
$=1-\left(\frac{1}{20}\right)=\frac{19}{20}$
Now the assembled product will not be defective if both the parts are not defective and hence the probability of this event
$=\frac{95}{104}\times \frac{19}{20}=\frac{19\times 19}{104\times 4}=\frac{361}{416}.$
[By the multiplication therorem.]