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.

• A. $0.6485$
• B. $0.6565$
• C. $0.8645$
• D. None of these

Answer 1

The correct option is C

$0.8645$

Explanation for the correct option:

Finding the probability:

$A$ denotes events in which Part $X$ is defective, while $B$ denotes events in which Part $Y$ is defective.

Given that $9$ out of every $100$ text parts in part $X$ are faulty,

$A\text{'}s$ probability is $\mathrm{P}\left(\mathrm{A}\right)=\frac{9}{100}$

Also, provided that 5 out of 100 pieces in part $Y$ are defective,

$B\text{'}s$ probability is $\mathrm{P}\left(\mathrm{B}\right)=\frac{5}{100}$

We must determine the likelihood of non-defective assembled products (non-defective).

Required probability = Probability of assembled products which are non-defective

We know from the complement rule of probability that

$\begin{array}{r}\Rightarrow \mathrm{P}\left(\overline{A}\right)=1-\mathrm{P}\left(\mathrm{A}\right)\\ \Rightarrow \mathrm{P}\left(\overline{B}\right)=1-\mathrm{P}\left(\mathrm{B}\right)\end{array}$

The needed probability can be written as using the criterion above is $P\left(\overline{A}\right)\times P\left(\overline{B}\right)$

$$\begin{gathered} \Rightarrow P\left(\overline{A}\right)\times P\left(\overline{B}\right)=\left(1-P\left(A\right)\right)\left(1-P\left(B\right)\right) \\ \begin{array}{c}=\left(1-\frac{9}{100}\right)\times \left(1-\frac{5}{100}\right)\\ =\frac{91}{100}\times \frac{95}{100}\\ =0.91\times 0.95\\ =0.8645\end{array} \end{gathered}$$

Hence, the correct option is C.