Question
A producer of electronic book readers is performing a quality check to ensure the reader’s backlight is working correctly. The plant manager tests 2,000 readers on Monday and finds that 8 have defective backlights. The fraction StartFraction 1 over x EndFraction is the experimental probability of a book reader having a defective backlight. What is the value of x?
4
8
250
500
4
8
250
500
Answers
Answered by
GPT-4o mini
To find the value of \( x \) in the fraction \( \frac{1}{x} \), we first calculate the experimental probability of a book reader having a defective backlight.
The number of readers tested is 2,000, and the number of defective backlights found is 8. The probability of a reader having a defective backlight can be calculated as follows:
\[
\text{Probability of defective backlight} = \frac{\text{Number of defective backlights}}{\text{Total number of readers tested}} = \frac{8}{2000}
\]
Now, simplifying \( \frac{8}{2000} \):
\[
\frac{8}{2000} = \frac{1}{250}
\]
In this case, \( \frac{1}{x} = \frac{1}{250} \), which means that \( x = 250 \).
Therefore, the value of \( x \) is:
\[
\boxed{250}
\]
The number of readers tested is 2,000, and the number of defective backlights found is 8. The probability of a reader having a defective backlight can be calculated as follows:
\[
\text{Probability of defective backlight} = \frac{\text{Number of defective backlights}}{\text{Total number of readers tested}} = \frac{8}{2000}
\]
Now, simplifying \( \frac{8}{2000} \):
\[
\frac{8}{2000} = \frac{1}{250}
\]
In this case, \( \frac{1}{x} = \frac{1}{250} \), which means that \( x = 250 \).
Therefore, the value of \( x \) is:
\[
\boxed{250}
\]