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.

Answer 1

Given,

An article manufactured by a company consists of two parts X and Y.

Part X has 9 out of 100 defective

That is, Part X has 91 out of 100 non defective

Part Y has 5 out of 100 defective

That is, Part Y has 95 out of 100 non defective

Consider, 

X = a non defective part of X

Y = a non defective part of Y

P(assembled product will not be defective)

P(neither X defective nor Y defective)

=P(X ∩ Y)

=P(X)P(Y)