An article manufactured by a company consists of two parts X and Y. In the process of manuifacture of the part X, 9 out of 100 parts may be defective. Similarly, 5 out of 100 are likely to be defective int he manufacture of the part. Y. Calculate the probability that the assembled product will not be defective.

Options

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

Answer

To solve the problem, we need to calculate the probability that the assembled product (which consists of parts X and Y) is not defective.

### Step-by-Step Solution:

1. **Determine the probability of part X being non-defective:**
- Given that 9 out of 100 parts X are defective, the probability of part X being defective is:
\[ P(\text{X defective}) = \frac{9}{100} \]
- Therefore, the probability of part X being non-defective is:
\[ P(\text{X non-defective}) = 1 - P(\text{X defective}) = 1 - \frac{9}{100} = \frac{91}{100} \]

2. **Determine the probability of part Y being non-defective:**
- Similarly, given that 5 out of 100 parts Y are defective, the probability of part Y being defective is:
\[ P(\text{Y defective}) = \frac{5}{100} \]
- Thus, the probability of part Y being non-defective is:
\[ P(\text{Y non-defective}) = 1 - P(\text{Y defective}) = 1 - \frac{5}{100} = \frac{95}{100} \]

3. **Calculate the probability that both parts X and Y are non-defective:**
- Since the events of parts X and Y being non-defective are independent, we can multiply their probabilities:
\[ P(\text{X non-defective and Y non-defective}) = P(\text{X non-defective}) \times P(\text{Y non-defective}) = \frac{91}{100} \times \frac{95}{100} \]

4. **Perform the multiplication:**
- Calculate:
\[ P(\text{X non-defective and Y non-defective}) = \frac{91 \times 95}{100 \times 100} = \frac{8645}{10000} \]

5. **Convert the fraction to decimal form:**
- To express the probability in decimal form:
\[ P(\text{X non-defective and Y non-defective}) = 0.8645 \]

### Final Answer:
The probability that the assembled product will not be defective is **0.8645**.