Question

An article manufactured by a company consists of 100 parts X and Y. In the process of manufacturing the part X. 9 out of 100 parts may be defective. Similarly 5 out of 100 are likely to be defective in part in part Y. calculate the probability that the assembled product will not be defective.

Answer 1

Hint: The probability for the not defective item for the item X and Y is to be calculated from the probability of defective item. Probability for any event A is given by, $ P(A) = \dfrac{m}{n} $ where, $ m = $ favorable outcome and $ n = $ total number of outcomes. The probability of a complimentary event, $P\left( {\bar A} \right) = 1 - P\left( A \right)$ .

Complete step-by-step answer:
Probability of defective item in X , $ P(X) = \dfrac{m}{n} $
Where, favorable outcome and total number of outcomes.
Probability of defective item in X , $ P(X) = \dfrac{9}{{100}} $
The probability for the non-defective item in X,
 $
  P\left( {\bar X} \right) = 1 - P\left( X \right) \\
  P\left( {\bar X} \right) = 1 - \dfrac{9}{{100}} = \dfrac{{91}}{{100}} = 0.91 \\
 $ .

Probability of the defective item in Y, $P(Y) = \dfrac{m}{n}$
Where,
 Number of favorable outcomes and Total number of outcomes.
Probability of the defective item in Y, $P(Y) = \dfrac{5}{{100}}$
The probability for the non-defective item in Y,
 $
  P\left( {\bar Y} \right) = 1 - P\left( Y \right) \\
  P\left( {\bar Y} \right) = 1 - \dfrac{5}{{100}} = \dfrac{{95}}{{100}} = 0.95 \\
 $ .
Probability of the assembled product from item X and Y,
$P(A) = $ (The probability for the non-defective item in X)*( The probability for the non-defective item in Y)
$
  P(A) = \left( {0.91} \right) * \left( {0.95} \right) \\
  P(A) = 0.8645 \\
 $

Hence, the probability of the assembled product is $ P(A) = 0.8645 $.

Note: The complementary events are those which have two outcomes like getting passed in the Exam and getting failed. The probability of them P (getting passed) + P (getting failed) = 1.
The formula for the complimentary event should be used for simplicity of calculation.