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 part $Y$. Calculate the probability that the assembled product will not be defective.

Answer 1

Let $A=$ Part $X$ is not defective

Probability of $A$ is $P\left(A\right)=\frac{91}{100}$

$B=$Part $Y$ is not defective.

Probability of $B$ is $P\left(B\right)=\frac{95}{100}$

Required probability $=P(A\cap B)=P\left(A\right)P\left(B\right)=\frac{91}{100}\times \frac{95}{100}=\frac{8645}{10000}$