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.

Home » An article manufactured by a company consists of two parts and . In the process of manufacture of part X. 8 out of 100 parts may be defective. Similarly, 5 out of 100 parts of may be defective. Calculate the probability that the assembled product will not be defective.

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.

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, $\mathrm{P}(\mathrm{X})=\frac{8}{100}$ and $\mathrm{P}(\mathrm{Y})=\frac{5}{100} \Rightarrow \mathrm{P}(\bar{X})=\frac{92}{100}$ and $\mathrm{P}(\bar{Y})$ $=\frac{95}{100}$
Here,
$\begin{array}{l} \text { P(product assembled will not be defective) }=1 \text { - P(product assembled to be defective) } \\ =1-[P(X \text { and not } Y)+P(Y \text { and not } X)+P(\text { both })] \\ =1-[P(X \cap \bar{Y})+P(Y \cap \bar{X})+P(X \cap Y)] \\ =1-[P(X) \times P(\bar{Y})+P(Y) \times P(\bar{X})+P(X) \times P(Y)] \\ =1-\left[\left(\frac{8}{100} \times \frac{95}{100}\right)+\left(\frac{5}{100} \times \frac{92}{100}\right)+\left(\frac{8}{100} \times \frac{5}{100}\right)\right] \\ =1-\left[\frac{760}{10000}+\frac{460}{10000}+\frac{40}{10000}\right] \end{array}$
$=\frac{437}{500}$
Therefore, The probability that the assembled product will not be defective is $\frac{437}{500}$ .