To determine the probability that any one car would have a defect in one of the headlight bulbs, given that 30,000 cars were produced and 222 were found to have this defect, we can use the following steps:
1. Determine the total number of cars:
[tex]\[ \text{Total number of cars} = 30,000 \][/tex]
2. Determine the number of cars with the defect:
[tex]\[ \text{Number of cars with defect} = 222 \][/tex]
3. Calculate the probability of a car having the defect:
This can be calculated by the ratio of the number of cars with defects to the total number of cars.
[tex]\[ \text{Probability (P)} = \frac{\text{Number of cars with defect}}{\text{Total number of cars}} = \frac{222}{30,000} \][/tex]
4. Express the probability as a fraction:
Simplify the fraction [tex]\( \frac{222}{30,000} \)[/tex] to its simplest form.
The simplified form of [tex]\( \frac{222}{30,000} \)[/tex] is [tex]\( \frac{37}{5000} \)[/tex].
Therefore, the probability that any one of the 30,000 cars would have a defect in one of the headlight bulbs is [tex]\( \frac{37}{5000} \)[/tex].
Checking against the given answer choices:
- A. [tex]\( \frac{1}{5200} \)[/tex]
- B. [tex]\( \frac{37}{5000} \)[/tex]
- C. [tex]\( \frac{2}{6235} \)[/tex]
- D. [tex]\( \frac{10}{520} \)[/tex]
The correct answer is:
[tex]\[ \boxed{\frac{37}{5000}} \][/tex]
Thus, the best answer for the question is:
[tex]\[ \text{B.} \frac{37}{5000} \][/tex]
