Answered

### 9-1: Experimental and Theoretical Probability

A quality control inspector samples 600 LCD monitors and finds defects in 3 of them. What is the experimental probability that a monitor selected at random will have a defect?

A. 5%
B. 2%
C. 0.5%
D. 0.2%



Answer :

Sure! Let's solve this step-by-step:

1. Identify the relevant data:
- Total number of monitors sampled: 600
- Number of defective monitors found: 3

2. Understand what experimental probability is:
The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials, typically expressed as a percentage.

3. Set up the ratio:
The probability of selecting a defective monitor is given by the ratio of defective monitors to the total number of monitors sampled.
[tex]\[ \text{Probability} = \frac{\text{Number of defective monitors}}{\text{Total number of monitors sampled}} \][/tex]
Substituting the given values:
[tex]\[ \text{Probability} = \frac{3}{600} \][/tex]

4. Simplify the ratio:
Simplifying the fraction, we get:
[tex]\[ \frac{3}{600} = \frac{1}{200} \][/tex]

5. Convert the ratio to a percentage:
To convert this fraction into a percentage, we multiply by 100:
[tex]\[ \text{Probability (in percentage)} = \left(\frac{1}{200}\right) \times 100 = 0.5\% \][/tex]

6. Determine the correct answer option:
The result is 0.5%, which matches option C.

Thus, the experimental probability that a monitor selected at random will have a defect is [tex]\( 0.5\% \)[/tex] or option C.