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

(a) 0.6485 

(b) 0.6565 

(c) 0.8645 

(d) None of these

Answer 1

(c) 0.8645

Required probability = P(X not defective and Y not defective) 

= P(\(\bar{X}\)) x P(\(\bar{Y}\))

= (1 – P(X)) (1 – P(Y))

= \(\bigg(1-\frac{9}{100}\bigg)\)\(\bigg(1-\frac{5}{100}\bigg)\)

= \(\frac{91}{100}\) x \(\frac{95}{100}\) = \(\frac{8645}{10000}\) = 0.8645.