Question
In a factory that manufactures tires, a machine responsible for molding the tire has a failure rate of 0.2%. If 1,000 tires are produced in a day, of which 6 are faulty, what is the difference between the experimental probability and the theoretical probability?
Answers
GPT-4o mini
To solve the problem, we'll calculate both the theoretical probability of a tire being faulty and the experimental probability based on the given data, and then find the difference between them.
1. **Theoretical Probability**:
The theoretical probability of a tire being faulty (failure rate) is given as 0.2%. This can be expressed in decimal form as:
\[
P(\text{faulty}) = 0.2\% = \frac{0.2}{100} = 0.002
\]
2. **Experimental Probability**:
The experimental probability is based on the actual number of faulty tires reported. There are 6 faulty tires out of 1,000 produced. Thus, the experimental probability is calculated as:
\[
P(\text{faulty, experimental}) = \frac{\text{Number of faulty tires}}{\text{Total number of tires}} = \frac{6}{1000} = 0.006
\]
3. **Difference between Experimental and Theoretical Probability**:
Now we find the difference between the experimental probability and the theoretical probability:
\[
\text{Difference} = P(\text{faulty, experimental}) - P(\text{faulty, theoretical}) = 0.006 - 0.002 = 0.004
\]
Thus, the difference between the experimental probability and the theoretical probability is **0.004**.
1. **Theoretical Probability**:
The theoretical probability of a tire being faulty (failure rate) is given as 0.2%. This can be expressed in decimal form as:
\[
P(\text{faulty}) = 0.2\% = \frac{0.2}{100} = 0.002
\]
2. **Experimental Probability**:
The experimental probability is based on the actual number of faulty tires reported. There are 6 faulty tires out of 1,000 produced. Thus, the experimental probability is calculated as:
\[
P(\text{faulty, experimental}) = \frac{\text{Number of faulty tires}}{\text{Total number of tires}} = \frac{6}{1000} = 0.006
\]
3. **Difference between Experimental and Theoretical Probability**:
Now we find the difference between the experimental probability and the theoretical probability:
\[
\text{Difference} = P(\text{faulty, experimental}) - P(\text{faulty, theoretical}) = 0.006 - 0.002 = 0.004
\]
Thus, the difference between the experimental probability and the theoretical probability is **0.004**.