A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?

Options

A. 0.06
B. 0.16
C. 0.84
D. 0.94

Explanation

To solve the problem, we need to find the probability that the machine will not stop working. This means that none of the parts A, B, or C should be defective.

### Step-by-Step Solution:

1. **Identify the probabilities of each part being defective:**
- Probability that part A is defective, \( P(A) = 0.02 \)
- Probability that part B is defective, \( P(B) = 0.10 \)
- Probability that part C is defective, \( P(C) = 0.05 \)

2. **Calculate the probabilities of each part not being defective:**
- Probability that part A is not defective, \( P(A') = 1 - P(A) = 1 - 0.02 = 0.98 \)
- Probability that part B is not defective, \( P(B') = 1 - P(B) = 1 - 0.10 = 0.90 \)
- Probability that part C is not defective, \( P(C') = 1 - P(C) = 1 - 0.05 = 0.95 \)

3. **Calculate the probability that the machine will not stop working:**
- The machine will not stop working if all parts are not defective. Therefore, we need to find \( P(A' \cap B' \cap C') \).
- Since the defects are independent events, we can multiply the probabilities:
\[ P(A' \cap B' \cap C') = P(A') \times P(B') \times P(C') = 0.98 \times 0.90 \times 0.95 \]

4. **Perform the multiplication:**
- First, calculate \( 0.98 \times 0.90 = 0.882 \)
- Then, calculate \( 0.882 \times 0.95 = 0.8361 \)

5. **Conclusion:**
- The probability that the machine will not stop working is approximately \( 0.8361 \), which can be rounded to \( 0.84 \).

### Final Answer:
The probability that the machine will not stop working is \( \approx 0.84 \).