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

$$\begin{gathered} \mathrm{Let}: \\ A=\mathrm{Particle}X\mathrm{is}\mathrm{defective} \\ B=\mathrm{Particle}Y\mathrm{is}\mathrm{defective} \\ \therefore P\left(A\right)=\frac{9}{100} \\ P\left(B\right)=\frac{5}{100} \\ \mathrm{Required}\mathrm{probability}=P\left(\overline{A}\cap \overline{B}\right) \\ =P\left(\overline{A}\right)\times P\left(\overline{B}\right) \\ =\left[1-P\left(A\right)\right]\times \left[1-P\left(B\right)\right] \\ =\left[1-\frac{9}{100}\right]\times \left[1-\frac{5}{100}\right] \\ =\frac{91}{100}\times \frac{95}{100} \\ =0.91\times 0.95 \\ =0.8645 \end{gathered}$$