To determine the value of [tex]\( x \)[/tex] for which the fraction [tex]\( \frac{1}{x} \)[/tex] represents the experimental probability of a book reader having a defective backlight, we need to follow these steps:
1. Find the total number of readers tested and the number of defective readers:
- Total readers tested: 2000
- Defective readers: 8
2. Calculate the experimental probability as a fraction:
The experimental probability [tex]\( P \)[/tex] of a book reader being defective is given by:
[tex]\[
P = \frac{\text{Number of defective readers}}{\text{Total number of readers tested}} = \frac{8}{2000}
\][/tex]
3. Simplify the fraction:
To find the value of [tex]\( P \)[/tex], we simplify the fraction:
[tex]\[
P = \frac{8}{2000} = \frac{1}{250}
\][/tex]
4. Determine the value of [tex]\( x \)[/tex]:
Since [tex]\( P = \frac{1}{250} \)[/tex], it is clear that the experimental probability is represented by [tex]\( \frac{1}{x} \)[/tex] where [tex]\( x = 250 \)[/tex].
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 250 \)[/tex].
