An article manufactured by a company consists of two parts X and Y. In the process of manufacture of part X. 8 out of 100 parts may be defective. Similarly, 5 out of 100 parts of Y may be defective. Calculate the probability that the assembled product will not be defective.
Given: X and Y are the two parts of a company that manufactures an article.
Here the probability of the parts being defective is given i.e, P(X) = 
and P(Y) = 
P(
) = 
and P(
) = 
To Find: the probability that the assembled product will not be defective.
Here,
P(product assembled will not be defective) = 1 – P(product assembled to be defective)
=1 – [P(X and not Y) + P(Y and not X) +P(both)]
= 1- [P( X 
) + P(Y 
) + P( X 
Y)]
= 1- [P(X) 
P(
) + P(Y) 
P(
) + P(X) 
P(Y)]
= 1-[ 
+ 
)+ 
]
=1- 
+ 
+ 
]
= 
Therefore, The probability that the assembled product will not be defective is 
.