To find out how many trials were performed during the experiment, we need to utilize the relationship between the number of successful outcomes, the experimental probability, and the total number of trials.
First, let's define our variables:
- Let [tex]\( R \)[/tex] be the number of times the spinner landed on red, which we know is 6 times.
- Let [tex]\( P \)[/tex] be the experimental probability of landing on red, which is given as [tex]\(\frac{1}{8}\)[/tex].
The experimental probability [tex]\( P \)[/tex] can be defined by the ratio of the number of successful outcomes (landing on red) to the total number of trials [tex]\( T \)[/tex]:
[tex]\[ P = \frac{R}{T} \][/tex]
We can rearrange this equation to solve for the total number of trials [tex]\( T \)[/tex]:
[tex]\[ T = \frac{R}{P} \][/tex]
Substitute the given values [tex]\( R = 6 \)[/tex] and [tex]\( P = \frac{1}{8} \)[/tex] into the equation:
[tex]\[ T = \frac{6}{\frac{1}{8}} \][/tex]
Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[ T = 6 \times 8 \][/tex]
Perform the multiplication:
[tex]\[ T = 48 \][/tex]
Thus, the total number of trials performed is:
[tex]\[ \boxed{48} \][/tex]
